CMG V 10,1, p marg. add. E 3. Unauthenticated Download Date 8/14/18 9:17 AM

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "CMG V 10,1, p marg. add. E 3. Unauthenticated Download Date 8/14/18 9:17 AM"

Transcript

1 شرح جالينوس للمقالة الثانية من كتاب ا بقراط المسم ى ا فيذيميا المقالة الا ولى CMG V 10,1, p. 155 المقالة الا ولى من تفسير جالينوس للمقالة الثانية من كتاب ا بقراط المسم ى 5 ا فيذيميا. ترجمة حنين بن ا سحق. قال ا بقراط: الجمر الصيفي الذي كان بقرانون: جاءت ا مطار جود مع حر الصيف كل ه وكان ا كثر ما يكون مع الجنوب ويصير تحت الجلد صديد فا ذا احتقن سخن وولد حك ة ثم كانت تخرج فيه نف اخات شبيهة بحرق النار وكان يخي ل ا ليهم ا ن ما دون الجلد يحترق احتراقا. 10 قال جالينوس: ا ن ا بقراط وصف في المقالة الا ولى ا مر ثلاث حالات من حالات الهواء حدثت عنها ا مراض ووصف في المقالة الثالثة من هذا الكتاب بعينه ا مر حال واحدة وبائي ة. فقد م ا و لا في وصف تلك الحالات كل ها صفة تغي ر الهواء المحيط بالا بدان وخروجه عن طبيعته ثم ا تبع ذلك بصفة طبائع الا مراض التي حدثت لكثير من الناس عن تلك الحالات. 156,15 17 v. Maǧūsī, Malakī I [الجمر احتراقا 6 9 4sq. للمقالة ا فيذيميا M: om. E, in marg. add. ترجمة ا سحق E 3 5 M: om. بقرانون E 6 M: E A: om. M ثم M A: om. E, in marg. add. E 2 حك ة A 8 صديدا E: صديد ا M: صديد Eىٯراىون 7 M: om. E, in تلك M: scripsi وثانية E: وىاىية [وبائي ة A 12 ىحرق M: E يحترق M 9 بحريق A: E بحرق marg. add. E 3 E ىكثره M: لكثير 14

2 GALEN COMMENTARY ON T HE SECOND BOOK OF HIPPOCRATES' EPIDEMICS PART I The first part of G a l e n 's Commentary on the second book of the work of H i p - p o c r a t e s called Epidemics. 1 Translation by Ḥ u n a y n i b n I s ḥ ā q. I 1 Hippocrates said [I 1: V 72,3 7 L.]: T h e s u m m e r c a r b u n c l e s t h a t o c - curred in Cranon: heavy rain fell in conjunction with heat throughout summer, mostly with southerly wind. Serous liquid develops under the skin, and when it becomes congested, it grows hot and produces itching. (The skin) then broke out in blisters that resembled a burn (caused) by fire. It gave them the impression that it burns under the skin. Galen said: H i p p o c r a t e s described in the first book three (sets of ) climatic conditions which cause diseases. In the third book of this same work he described a single condition that induced epidemic diseases. He first presented in the description of all these conditions an account of the change of the air surrounding the bodies and its deviation from its nature and then added a description of the natures of the diseases that many people had as a result of these conditions. 1 Here and elsewhere in the text, the title of the Epidemics is transliterated as ifīḏīmiyā.

3 78 Galen, Commentary on the second book 156 ولم يفعل ذلك في هذه المقالة على هذا المثال لكن ه ذكر ا و لا المرض الذي حدث ثم ذكر الوقت الذي حدث فيه من ا وقات السنة ثم ذكر البلد الذي حدث فيه ثم ذكر مزاج ذلك الوقت والخلط الذي تول د في ا بدان الناس عن ذلك المزاج ثم وصف طريق فعل ذلك الخلط الذي به حدث السبب المول د للجمر ثم ذكر 5 العرض الذي تقد م ذلك والعرض الذي كان معه في تلك الحال والعرض الذي حدث فيه بعد تزي ده والعرض الذي حدث فيه عند بلوغه منتهاه. والسبب في تقديمه ذكر المرض على خلاف عادته ثم ثنى به فذكر حال الهواء قصده للا يجاز فقد نجد الواضع لهذه المقالة ا بقراط نفسه كان ا و ثاسالوس ابنه حريصا على الا يجاز. ولا فرق عندي فيما نحن بسبيله بين ا ن يقال ا ن هذا الكتاب 10 لا بقراط وبين ا ن يقال ا ن ه لثاسالوس. وا نا ملخ ص هذه الا شياء التي ذكرتها مجملا فا قول ا ن فاتحة هذه المقالة كا ن ه جعلها شبيهة بما تقد م من الرسم قبل الشيء الذي يقصد لصفته كا ن ه قال: «ا ن الجمر الذي حدث في الصيف بمدينة قرانون» ثم تقطع ا ذا قرا ت هذا وتبتدئ من الرا س وتقرا : «جاءت ا مطار جود» حت ى تفهم في هذا الكلام الا و ل من عندك 15 ا ن ه كان على هذه الجهة كا ن ه قال: «ا ن الجمر الصيفي الذي كان بقرانون كان على هذه الجهة: جاءت ا مطار جود مع حر الصيف كل ه وكان ا كثر ما يكون تلك الا مطار مع الجنوب». والخلط M 3 post التي حدثت E: الذي حدث E 2 II الامراض التي حدثت M: المرض حدث 1sq. I حدث M post احدث E: حدث E ذلك add. فعل E 4 ante المرار M: المزاج M الردي add. والعرض iter. بلوغه E post عند تدىيره M: بعد تزي ده E 6 ىىٯدم M: تقد م M 5 المولد del. add. et scriptum sine dubio للايجاز suspicor [للا يجاز M 8 ثني بذكر :E فذكر E 7 الذى حدث فيه عند in alio [ملخ ص M 11 لتاسالوس E: لثاسالوس M لبقراط E: لا بقراط Colv. 10 in marg. scr. ىلايجان E: هذا E 14 ٯرابيون M: قرانون M 13 ذكر add. مجملا in marg. scr. Colv. ante مڡح ض vel مبخ ص om. بقرانون M 15 M: ىٯرابيوں كل ه E 16 M: om. E

4 of Hippocrates Epidemics part I But he did not proceed in this manner in this book. Rather, he first discussed the disease which occurred; then the season when it occurred; then the location where it occurred; then the mixture of this season and the humour that was generated in people's bodies by this mixture. He then described the workings of the humour that brought about the cause which produced the carbuncles. He then mentioned the symptom which preceded them, the symptom which accompanied them in this condition, the symptom that occurred after its increase and the symptom that occurred when it reached its climax. The reason why he mentions the disease first contrary to his usual practice and then turned around and mentioned the climatic conditions is that he wants to be concise; we in fact find that the author of this book, whether it be H i p p o c r a t e s himself or his son T h e s s a l u s, strives to be concise. It makes no difference for me in our present endeavour whether one says that this book is by H i p p o c r a t e s or T h e s s a - lus. I shall briefly explain the things I have mentioned. I say that he seems to have framed the opening of this book like a headline that precedes the thing he wants to describe, as if he had said: the carbuncles that occurred in summer in t h e c i t y o f C r a n o n ; you then stop after reading this, start from the top and read: h e a v y r a i n fe l l, so that you understand the beginning of this passage as follows, (namely) as if he said: the summer carbuncles that occurred in C r a n o n arose in the following way: heavy rain fell in conjunction with heat throughout summer, mostly with southerly wind.

5 80 Galen, Commentary on the second book «والجمرة» هي قرحة تكون من تلقاء نفسها وعليها خشكريشة في ا كثر الا مر سوداء ورب ما كانت بلون الرماد. ويكون معها في المواضع التي تحيط بها حرارة شديدة حت ى يحس من يلمسها منها بحرارة كثيرة فضلا عن ا ن يحس ها صاحب القرحة. والمواضع ا يضا التي حول الخشكريشة ليست بصادقة الحمرة كما يكون 5 في الورم الحار الذي يسم ى «فلغموني» لكن ه يكون مائلا ا لى السواد والصلابة ا يضا فيه ا زيد كثيرا. وعلى هذه الصفة را ينا نحن الجمر الذي حدث بكثير من الناس بمدينة برغامس ورا ه غيرنا في سائر مدن ا سيا كل ها ا ل ا الخطاء كالذي خب رنا به من را ه. ولهذا منذ كان ا ربعون سنة لم ير فيها حدوث عام ا خر شبيه بذلك من هذا الجمر. وكان ذلك 10 الجمر الذي كان بعقب حال من الهواء جنوبي ة رطبة مع سكون من الرياح. وهذه هي جملة صفة الحال التي وصفها ا بقراط ا يضا فا ن ه قال: «ا ن ه جاءت ا مطار جود مع حر الصيف كل ه». وحدوث المطر «في الصيف كل ه» خارج عن المجرى الطبيعي ولا سي ما ا ذا كان المطر «جودا». فا ن ذلك لو كان في الشتاء لجعل مزاجه مزاجا رديئا فا ن كان Ḥunayn, v. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 141 v r 3. [والجمرة كثيرا 1 6 Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r sq. كل ه [ا ن ه. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r 13 13sq. رديئا [ولا. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r 13sq. السبب 14 82,2 [فا ن. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r 14sq. b. والمواصع الىى M: والموضع ايض ا الذي E: والمواضع التي Colv. 4 supra lin. scr. منها in alio [معها 2 Riḍwān ليست بصادقة E b. Riḍwān: ليس بصادق M, in alio ليست بصادقة in marg. scr. Colv. 5 E: برغامس b. Riḍwān 7 المسمى M: E الذي يسم ى M b. Riḍwān: om. E, in marg. add. E 2 الحار M, asia in marg. scr. Colv.: scripsi اسيا E: اثينا [ا سيا M بلد add. ا سيا M 8 ante برعاميس Colv. in marg. scr. حوا vel [جودا M 14 الام ر E: المجرى M 13 امطور E: ا مطار 11

6 of Hippocrates Epidemics part I A c a r b u n c l e is an ulceration which occurs spontaneously. It is covered by a scab that is in most cases black but may also be the colour of ashes. It is accompanied in the areas surrounding it by such an intense heat that (even) someone who touches it, not to mention the person suffering from the ulcer, feels a strong heat. The areas around the scab are also not genuinely red as in (the case of ) the inflammation called phlegmony 1 but somewhat blackish, and they are much harder, too. We have seen carbuncles of this kind that affected many people in the city of P e r - gamum. Others have seen them in almost all other cities in Asia, as those who observed them told us. For forty years no other general outbreak of these carbuncles like this has been seen there. The carbuncles that appeared came immediately after southerly, wet weather with still air. This is on the whole the description of the condition Hippocrates also gave; he said: heavy rain fell in conjunction with heat throughout summer. That rain occurred t h r o u g h o u t s u m m e r is unnatural, especially if the rain was h e a v y. If this happens in winter, it would corrupt its mixture. If it is also hot, 1 transliterated here and in the following as falġamūnī

7 82 Galen, Commentary on the second book مع ذلك حر ا ا عني ا ل ا تهب رياح قوي ة فا ن الحر لا يكون في الصيف ا ل ا بهذا السبب فا ن الا فة تكون ا عظم. وذلك ا مر قد كان عرض بقرانون فا ن ه قد كانت الرياح في ذلك الوقت وا ن هب ت في الا حايين فا ن ها ا ن ما كانت تكون «جنوبي ة». وهذه الريح من ا عون الرياح على ا رخاء قو ة البدن كما وصف ا بقراط في كتاب 5 الفصول وعلى ا ن تحدث ا مراض العفونة. وقرانون ا يضا هي مدينة من بلاد ثساليا من قبل ا ن ها في وهدة وهي ا يضا مع ذلك في ناحية الجنوب توافق ما كانت عليه تلك الحال من الا فراط. ولذلك وقت تلك الحال من ا وقات السنة الذي دل عليه بقول «الجمر الصيفي «يعني الجمر الذي كان حدث في الصيف على ا ن قوما فهموا من قوله هذا لا ا ن ه كان في ذلك الوقت بل ا ن ه يكون كذلك دائما وا ن هذا ا مر خاص لتوليد الجمر. ولا فرق في ذلك الجمر الذي كان في ذلك الوقت ا ذا كان تول د الجمر ا ن ما شا نه ا ن يكون في الصيف ا و كان ا ن ما حدث بقرانون في الصيف. فا ن الذي يكتفي به هذا فقط ا ن تعلم من ا مر حدوثه ا ن مزاج الهواء الذي حدث فيه كان حار ا عديما للرياح رطبا. فقد نرى عيانا ا ن جميع الا جسام تعفن وهذه 4sq.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r 15sq. [فا ن ه العفونة b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 r [العفونة Hipp.. [وهذه البدن 4 وقرانون 5sq. Aphor. III 5: p. 400,1sq. Magdelaine = IV 488,1sq. L.: Buqrāṭ, Fuṣūl 20,6sq. 16sq.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r [الجنوب scr. sine punctis in marg. الالڡ M, in alio sic الا حايين E 3 ىقراىون M: بقرانون M 2 حره E: حر ا 1 [ثساليا M وهي E: هي E وڡراىىوں M: وقرانون E 5 حىوبيا M: جنوبي ة ut vid., E,الاخاىں Colv.: تساليا sed Thessalia et aut semper in esse in Italia تساليا M, scribendum ايطاليا E: ايطالىا in marg. scr. Colv.: ايطاليا Ḥunayn, طشاليا Thessalia non Italia in marg. scr. Colv.: conieci 6 ante I في add. et del. وهي M post عليه add. بالحال E 8 post ولذلك add. ايض ا M الذي M: التي E M: om. E ا و الصيف M: correxi 12 II ا ذ E: اذ [ا ذا M لتولد E: لتوليد M 11 في ق و له E: بقول M: om. E ا ن M م ن ه E: فيه M 14 هوا E: هذا M: correxi 13 بقرنون E: om. [بقرانون

8 of Hippocrates Epidemics part I that is, no strong winds blow this is the only reason why heat occurs in summer, the harm would increase. This is what happened in C r a n o n : even if winds blew occasionally, they were at that time solely s o u t h e r l y. This is, as H i p p o c r a t e s said in his Aphorisms, one of the most effective winds in relaxing the strength of the body and causing diseases of putrefaction. Also, C r a n o n is a city in T h e s s a l y. Because it is situated in a depression and furthermore, in addition to this, faces southward, it reflects the extremes intrinsic to its condition. This is why the season of this condition is the one he indicated by saying t h e s u m m e r c a r b u n c l e s, that is, the carbuncles that occurred in summer. Some people, however, understood his words (to mean) not that they occur in that (particular) season, but that this is always the case and that this is typical of the generation of carbuncles. 1 But for the carbuncles that occurred in that season it does not make any difference whether carbuncles are normally only generated in summer or they only occurred in C r a n o n in summer. It is enough for you to know only this about their occurrence: the mixture of the air they occurred in was warm, windless and wet. We see with our own eyes that all 1 i.e. these carbuncles occur not just during that particular summer but they typically appear every summer

9 84 Galen, Commentary on the second book عند هذه الحال وا ن لم نعلم السبب في ذلك. ا ل ا ا ن ا بقراط قد بي ن السبب في ذلك بقوله «ويصير تحت الجلد صديد فا ذا احتقن سخن». فا ن معنى قوله «احتقن» ا ن ما هو ا ن ه بقي في البدن داخلا فلم يستفرغ استفراغا ظاهرا للحس ولا استفراغا خفي ا لكن ه لبث داخلا فعفن ومن قبل ذلك سخن سخونة خارجة عن 5 الا مر الطبيعي. فلم ا كان ذلك «ولد» ا و لا «حك ة» والحك ة تكون من ا خلاط لم تسخن سخونة شديدة جد ا لكن ها قد ابتدا ت ا ن تسخن. فلم ا تمادى به الزمان ونفذ ا رق ما كان في ذلك الخلط الذي عفن من ا سخف ا جزاء الجلد بسهولة واجتمع تحت الصفيحة الخارجة منه لكثافتها ولد «النف اخات». فا م ا الشيء الا غلظ من ذلك 10 الخلط فا ن ه لم ينفذ ا لى ا ن يبلغ ا لى الصفيحة الخارجة من الجلد لكن ه احتقن داخلا تحت الجلد واجتمع هناك فعفن وسخن سخونة شديدة حت ى «كان يخي ل ا لى صاحبه ا ن ما دون الجلد يحترق احتراقا». ثم من بعد هذا فا ن النف اخات كانت تتمد د من كثرة الرطوبة التي فيها وتتا ك ل من حد تها فتنقص. والجلد الذي من تحتها كان يحترق من ذلك الخلط المفرط الحر فيحدث منه فيه شبيه 15 بالخشكريشة التي تحدث من الكي. وهذه الا شياء ا شياء تعم جميع الجمر. فلم ا 6sq.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r 18sq. [بقي فعفن 3sq sq.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r [تسخن b. v. [فلم ا الكي Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 r 7 16 II 1: Ambrosianus B 135 sup., fol. 119 r Am-. Ḥunayn, Ǧawāmiʿ II 1: [ثم الجمر brosianus B 135 sup., fol. 119 r B 135 sup., fol. 119 r 30sq.. Ḥunayn, Ǧawāmiʿ [فلم ا شديدة sq. حد تها [فا ن. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus 2 post ذلك add. الوقت ا ن ما هو E 3 E: om. ومن M 4 M: من E 6 [حك ة supplend فو لد ىحك ه in marg. scr. ونفذ Colv. 7 M: ڡنفد كان E 8 M: om. E من M: om. E 9 ante لكثافتها add. et del. لكا ينفذ M 10 E: يبق واجتمع M 11 E: اجتمع تتمد د M 13 E: تمدد M تناكل [وتتا ك ل in marg. scr. Colv. 14 post الحر add. et del. التي ىحدث M 15 E: om. M ا شياء M المكي E: الكي

10 of Hippocrates Epidemics part I structures putrefy in this condition, even if we do not know the reason why. H i p p o - c r a t e s on the other hand explained the reason why by saying: s e r o u s l i qu i d d e - velops under the skin, and when it becomes congested, it grows hot. By saying it becomes congested, he means that it remained inside the body and was not excreted, neither in an obviously perceptible nor in a concealed manner. Rather, it stayed inside and putrefied, and because of this it became unnaturally hot. W hen this happened, it first p r o d u c e d i t c h i n g. Itching is caused by humours which have not warmed up very much but have started to warm up. After some time had passed and the finest components of this putrefied humour had easily penetrated the most porous parts of the skin and accumulated beneath its outer layer because of its thickness, they produced b l i s t e r s. Anything thicker than this humour did not pass through until it reached the outer layer of the skin but became congested inside underneath the skin and accumulated there. It then putrefied and grew very hot so that it gave the person suffering from it the impression that it b u r n s u n d e r t h e s k i n. Then, after this, the blisters expanded because of the abundant liquid they contained, (then) corroded because of its sharpness and shrank. The skin underneath them was burning because of this extremely hot humour. It then produced on it something like the scab caused by a burn. These things are common to all carbuncles.

11 86 Galen, Commentary on the second book 158 وا م ا الا شياء التي خص ت ذلك الجمر الذي حدث في ذلك الوقت فكانت شد ة ا فراط الحرارة التي فيما دون الجلد وتول د النف اخات. وا ن ه ليس يجب ضرورة ا ن يتقد م حدوث الجمر حدوث النف اخات ولذلك عب ر ا بقراط عن هذه المعاني با لفاظ مختلفة الا زمان. فوصف الا عراض التي تعم الجمر بحدوثها دائما با لفاظ تدل على 5 الوقت الحاضر منها قوله «ويصير تحت الجلد صديد» وقوله «فا ذا احتقن سخن وولد حك ة». فا م ا الا عراض التي خص ت ذلك الجمر الذي كان في ذلك الوقت فلم يعب ر عنها بمثل هذه الا لفاظ لكن ه عب ر عنها با لفاظ تدل ا ن ها ا ن ما عرضت مع ذلك الجمر فقط من ذلك ا ن ه قال في النف اخات: «كانت تخرج فيه نف اخات» وقال في الحرارة الخارجة عن الا مر الطبيعي : «وكان يخي ل ا ليهم ا ن ما دون الجلد 10 يحترق احتراقا.» والعجيب ا ن هذه النسخة يعرفها جميع القدماء ولا يزال من فس ر هذا الكتاب يبحث عن السبب الذي دعا ا بقراط ا لى ا ن يستعمل ا لفاظا تدل على ا زمان مختلفة. وتقد م ا رطاميدوروس وا صحابه على ا ن غي روا هذه الا لفاظ فجعلوها كل ها تدل على زمان واحد على هذا المثال: «وكان يصير تحت الجلد صديد وكان ا ذا 15 احتقن سخن وولد حك ة». وا نا مجمل قولي من ا و له ثم ا قطعه فا قول ا ن ا بقراط دل بقوله «جاءت ا مطار جود مع حر الصيف كل ه وكان ا كثر ما يكون مع الجنوب» على السبب الذي يسم ى «البادئ» الذي منه يكون تول د الجمر وهذا السبب هو سبب خارج عن scr. in marg. في ما E M, in alio فيها [فيما E 2 حصب Colv.: in marg. scr. خصب M, in alio خص ت 1 Colv.: scripsi وا ن ه M: فانه بحدوثها E 4 E: بح ر ورتها M 5 ante الوقت add. ذلك M الحاضر M: :E ارطاميدوس [ا رطاميدوروس M 13 است عمال الفاظ :E ا ن ا لفاظا M 12 ان ما :E ا ن ما E 9 الخاص add. ا بقراط M ante منذ E: من M, Artemidorus puto in marg. scr. Colv.: correxi 16 ارطامندوس M من E: عن M 18 قول

12 of Hippocrates Epidemics part I The things that are specific to the carbuncles that occurred at that time were the extreme, excessive heat underneath the skin and the generation of blisters. It is not absolutely necessary that carbuncles occur before blisters, and this is why H i p p o - c r a t e s expressed these concepts with verbs in different tenses: he described symptoms that always occur in all carbuncles with verbs that indicate the present tense, for example by saying serous liquid develops under the skin and when it becomes congested, it grows hot and produces itching. He did not express the symptoms typical for the carbuncles that occurred at that time with such verbs but expressed them with verbs that indicate that they occurred only with these carbuncles. For example, he said about the blisters: ( t h e s k i n ) t h e n b r o k e o u t i n b l i s t e r s, and he said about the unnatural heat: i t g a ve t h e m t h e i m p r e s - sion that it burns under the skin. It is amazing that all ancient authors know this wording, and the commentators of this book kept looking for the reason which led H i p p o c r a t e s to use verbs that indicate different tenses. A r t e m i d o r u s and his colleagues on the other hand went ahead and changed these verbs and made them all indicate the same tense as follows: serous liquid developed under the skin, and when it became congested, it grew hot and produced itching. I shall (now) sum up what I have said from the beginning and then conclude. I say that H i p p o c r a t e s indicated with his words h e a v y r a i n fe l l i n c o n j u n c t i o n with heat throughout summer, mostly with southerly wind the so-called procatarctic 1 cause that brings about the generation of the carbuncles. This 1 lit. which starts

13 88 Galen, Commentary on the second book الا بدان التي نالتها الا فة. ودل بقوله «ويصير تحت الجلد صديد» على السبب الذي يسم ى «المتقادم» الذي منه يكون تول د الجمر وهو السبب الذي يحدث في البدن ا و لا. ودل بقوله «فا ذا احتقن سخن» على الجهة التي بها يحدث ذلك السبب الجمر وذلك هو ا فراط حرارة الخلط الغالب في البدن وغليانه بسبب 5 العفونة. وسم اه «صديدا «من قبل ا ن ه كان خارجا عن الطبيعي ة خروجا رديئا خبيثا. فا م ا قوله «وولد حك ة» فهو عرض يتقد م حدوث الجمر. فا م ا ما بعد هذا فا عراض لزمت ذلك الجمر خاص ة الذي حدث في ذلك الوقت وهي حدوث «النف اخات الشبيهة بحرق النار» وا حساس من الحرارة الشديدة فيما دون الجلد حت ى «يخي ل» ا لى صاحب القرحة «ا ن ذلك الموضع منه يحترق 10 احتراقا». وقد تقد م فدل على ا ن ه يحدث منه ا ذا قرحة ذات خشكريشة منذ ا و ل كلامه حين قال: «الجمر الصيفي الذي كان بقرانون». فا ن اسم «الجمر» ا ن ما يدل على قرحة هذه حالها مع التهاب يكون حولها كما قلت. قال ا بقراط: ا ذا كان حر ولم يكن معه مطر لم يحدث في الحم يات عرق في ا كثر الا مر. فا ن جاء شيء من المطر في الحر ولو يسير كان العرق في الحم يات 15 ا كثر. فا عراض sq.. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 r [وسم اه خبيثا Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r [الجلد ويصير تحد الجلد صديدا على السبب الذ<ي يسمى المتقادم> الذي منه,E :M om. ويصير بقوله 3 1 :M صديد in marg. add. E 2 1 يكون تولد الجمرة وهو السبب الذي يح<دث في البدن> اولا ودل بقوله om. E, صديدا in marg. add. الجمر E 2 7 M: الحمى وهي E 8 E: وهو M واحساسا [وا حساس E: M جاءت : 2 om. E, in marg. add. E ذات M من هذا E: منه ا ذا M: correxi 10 ولحساس E ىٯراىون M: بقرانون 11

14 of Hippocrates Epidemics part I cause is external to the bodies which are harmed. By saying s e r o u s l i qu i d d e v e l - o p s u n d e r t h e s k i n, he indicated the so-called predisposing cause that brings about the generation of the carbuncles. This is the cause that occurs first in the body. By saying when it becomes congested, it grows hot, he indicated the way in which this cause brings about carbuncles, namely the extreme heat of the humour that dominates the body; its fervor is caused by putrefaction. He called it s e r o u s l i qu i d because it is unnatural in a bad and malignant manner. His words a n d g e n - e r a t e s i t c h i n g (denote) a symptom which precedes the occurrence of the carbuncles. What follows are symptoms that specifically attended the carbuncles that occurred at that time, namely the occurrence of b l i s t e r s t h a t r e s e m b l e d a b u r n ( c a u s e d ) b y f i r e and the sensation of intense heat under the skin so that it g a v e the people suffering from the ulceration t h e i m p r e s s i o n t h a t t h e a r e a b u r n s. He previously indicated that this then causes an ulceration with a scab at the beginning of his remark when he said: t h e s u m m e r c a r b u n c l e s t h a t o c - c u r r e d i n C r a n o n. The term c a r b u n c l e s indicates, as I said, an ulceration in this condition that is accompanied by an inflammation around it. I 2 Hippocrates said [I 2: V 72,8sq. L.]: I f t h e r e i s h e a t w i t h o u t r a i n, there is in most cases no sweating during fevers. If some rain falls during the heat, even only a small amount, there is more sweating during fevers.

15 90 Galen, Commentary on the second book قال جالينوس: ا ن هذا القول من ا بقراط قول ينتفع به من علمه مفردا على حدته في ا ن يتقد م فينبئ بالعرق الحادث فا ن تقدمة المعرفة بالعرق الكائن في الا مراض تكون من ا علام كثيرة وا حد تلك الا علام هو الذي وصف. وفي هذا القول ا يضا دليل شاهد على صح ة القول المتقد م الذي قال فيه: 5 «ويصير تحت الجلد صديد فا ذا احتقن سخن». وذلك لا ن ه متى كان مزاج 159 الهواء يابسا انفش ت ونفدت الرطوبات التي في البدن ومتى كان مزاج الهواء رطبا اجتمعت تلك الرطوبات فلم تنحل. وتلك الرطوبة تخرج من البدن في ا وائل الحم يات لا على طريق البحران فا ن البحران لا يكون دون ا ن تنضج الا خلاط التي في البدن لكن ها ا ن ما تخرج من قبل ا ن البدن لا يطيق ا ن يحويها لكثرتها حت ى 10 تفيض وتندفق. ولذلك ا ضاف قوم ا لى هذا القول شيئا مم ا يتلوه وهو قوله «في ا وائل الا مر» فجعلوه ا خر هذا الكلام وقوم جعلوا ذلك ا و ل الكلام الذي يتلو هذا على هذا المثال: قال ا بقراط: منذ ا وائل الا مر البحران يكون مع هذا ا عسر مم ا يكون مع غيره ا ل ا ا ن ه على حال يكون ا قل عسرا متى كان بسبب هذا ولم يكن بسبب حال المرض. 1 7 v. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 v [متى وتندفق II من E: مع M علمه M: عمله ٯٮٮى [فينبئ E 2 E: فيبسي M, in uno فيسي in alio ڡىىي sine punctis scribendum فبي ن in marg. scr. Colv.: ا علام correxi 3 E: الاعلام ا يضا M 4 M: om. E, in marg. add. في E يبست Colv.: in marg. scr. يبست M b. Riḍwān, in alio انفش ت M 6 انه E: لا ن ه E 3 5 لا وايل :E في اول :M في ا وائل M تتحل ل Riḍwān: E.b تنحل.b Riḍwān 7 ىىولد مىها العرق :M E البدن b. Riḍwān 8 post الحم يات add. بالعرق b. Riḍwān فا ن البحران M b. Riḍwān: والبحران Ε 11 M عسر A: E ا عسر M ان add. يكون E 13 ante I التي M: الذي

16 of Hippocrates Epidemics part I Galen said: H i p p o c r a t e s ' observation by itself helps the person who knows it to predict the occurrence of sweating. The prognosis of sweating in diseases is based on many signs, and one of these is as described. This passage also contains evidence that corroborates 1 the preceding one, in which he said: serous liquid develops under the skin, and when it becomes congested, it grows hot. For when the mixture of the air is dry, the liquids in the body are reduced and depleted, but when the mixture of the air is moist, these liquids accumulate and are not dissipated. These liquids emerge from the body at the beginning of fevers not by way of a crisis 2 the crisis does not take place before the humours in the body are concocted but because the body is unable to contain them owing to their large quantity, so that they overflow and pour out. Some people therefore added part of the following passage to this one, namely his words a t t h e b e g i n n i n g, and made them the end of this passage, while others made them the beginning of the next one in the following manner: I 3 Hippocrates said [I 2: V 72,10sq. L.]: At the beginning the crisis is more difficult in this case than otherwise, but it is still less difficult when it is caused by this rather than by the condition of the disease. 1 lit. that attests to the correctness of 2 i.e. they do not indicate or coincide with a crisis

17 92 Galen, Commentary on the second book قال جالينوس: يعني ا ن ا مراض من يصيبه العرق «منذ ا و ل» مرضه يكون البحران فيه لا محالة عسرا ا ل ا ا ن ما كان منها كذلك «بسبب حال المرض» «فعسر» البحران فيه «ا زيد» وما كان ا ن ما يحدث فيه منها العرق «في ا و له» من قبل الهواء «فعسر» البحران فيه «ا قل «يعني ا ن مد ة هذه الا مراض وتطاولها تكون ا قل. 5 قال ا بقراط: الحم يات المحرقة تكون في الا وقات الحار ة ا كثر وقد تكون في سائر الا وقات ا ل ا ا ن ها في الصيف تتزي د يبسا. قال جالينوس: ا ن ا نجد في بعض النسخ «<في> الا وقات الحار ة» ونجد في بعضها «في الا وقات الصيفي ة» ولا فرق بين الا مرين لا ن المعنى في هذا القول معنى واحد وهو المعنى الذي وصفه في كتاب الفصول كل ي ا وجزئي ا ا م ا الكل ي 10 فقوله: «والا مراض كل ها تحدث في ا وقات السنة كل ها ا ل ا ا ن بعضها في بعض الا وقات ا حرى ا ن يحدث ويهيج» وا م ا الجزئي فقوله: «فا م ا في الصيف فيعرض بعض هذه الا مراض ومحرقة». فا م ا ما قاله في ا خر هذا الكلام وهو قوله: «ا ل ا ا ن ها في الصيف تتزي د يبسا «فهذا معناه لقول ا ن الحم ى المحرقة ا بدا حار ة يابسة ا ل ا ا ن ها في الا وقات الحار ة 1 4 II ا قل [ا مراض. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 v Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r sq. ويهيج [والا مراض Hipp. Aphor. III 19: p. 405,6sq. Magdelaine = IV 494,13 15 L.: v. Buqrāṭ, Fuṣūl 24, sq. ومحرقة [فا م ا Hipp. Aphor. III 21: p. 406,1sq. Magdelaine = IV 494,20 495,1 L.:. Buqrāṭ, Fuṣūl 25,5sq. Ǧa-. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 v Ḥunayn, [ا ن وتنفد 14 94,2 wāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r 34sq. تكون E 5 ante I ڡيها Riḍwān: M b. فيه E 4 منه فيها M: فيه منها E 3 عسر Riḍwān: M b. عسرا 2 add. قد بعض A 7 M: om. E II في فيعرض addidi 11 E: فيتعرض M 12 ante ومحرقة add. M تزيد E: تتزي د Buqrāṭ, Fuṣūl 13 وحم يات دائمة

18 of Hippocrates Epidemics part I Galen said: He means that in the diseases of people who sweat a t t h e b e g i n - n i n g of their disease the c r i s i s is bound to be difficult, but that the crisis is m o r e d i f f i c u l t in those (diseases) in which this happens because of the c o n d i t i o n o f t h e d i s e a s e. In those (diseases) in which sweating occurs a t t h e b e g i n n i n g only because of the weather the crisis is l e s s d i f f i c u l t, that is, these diseases last and persist for a shorter time. I 4 Hippocrates said [I 2: V 72,11 13 L.]: B u r n i n g fe v e r s o c c u r m o r e f r e - quently in hot seasons. They may (also) occur in other seasons, but in summer they are drier. Galen said: We find in some copies i n h o t s e a s o n s and in others in summery seasons, but there is no difference between the two because they have the same meaning in this passage, namely the one he described in the Aphorisms in general and in particular: in general by saying all diseases occur at all seasons but some are more likely to occur and be stirred up in certain seasons, and in particular by saying in summer some of these diseases and burning (fevers) appear. What he said at the end of this passage, namely but in summer they are d r i e r, has the following meaning: burning fever is always hot and dry, but it is even

19 94 Galen, Commentary on the second book الصيفي ة تكون ا زيد يبسا لا ن الرطوبة التي في ا بدان ا صحابها من حرارة تلك الا وقات تنفش وتنفد. 160 قال ا بقراط: ا كثر ما يتول د السبعي ووجع الفؤاد في الخريف. قال جالينوس: ا ن في وقت الفواكه خاص ة يتول د من فساد ما يؤكل منها ومعها 5 من الا طعمة ا نواع الدود في البطن وهي ثلاثة ا حدها رقيق يكون فيما يلي الدبر شبيه بدود الخل والا خر غليظ مستدير شبيه بالحي ات يكون في الا معاء الرقاق والا خر عريض في جوفه قطع شبيه بحب القرع يكون في الا معاء الغلاظ. وا راد بقوله ا بقراط ا ن يحصر هذه الا نواع الثلاثة في اسم واحد فسم اها «السبعي «يعني الحيوان الخبيث. وقد قال قوم ا ن ه يريد «بالسبعي «الجذام لا ن 10 اليوناني ين يسم ون الجذام باسم «الفيل» والفيل ا حد الحيوانات الخبيثة المستطعمة فا ن الجذام ا يضا ا كثر ما يكون في الخريف. وقال قوم ا ن ه يريد «بالسبعي «الوسواس السوداوي لا ن تلك العل ة لا تجعل صاحبها في بدنه شبيها بالسبع كما يفعل الجذام لكن في نفسه ورا يه. وقال قوم ا ن ه يريد «بالسبعي «السرطان لخبث السرطان وصعوبة ا مره. وقال قوم ا ن ه يريد شيئين من هذه ا و ا شياء منها ا و كل ها. ويجب ا نواع sq.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r [ا ن البطن 4sq. 93: v. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 v b. Maymūn, Fuṣūl IX [الغلاظ Medical Aphorisms II 79,1sq. (Ar.) Bos E وهو M: وهي ut vid., corr. E 2 5,فيه M: ex من in marg. scr. E 3 فعله المقابلة [قال جالينوس 4 p. 125 coni. Garofalo, I commenti, شبيهة Riḍwān: E M b. شبيه E 7 ما Riḍwān: M b. فيما vid., ut,الس وراي E: ex السوداوي M 12 الم س ت عصبة E: المستطعمة M 10 ابقراط بقوله E: بقوله ا بقراط 8 corr. M, السوىاي in marg. scr. Colv. لا ن تجعل E: لا ان تلك العلة ٮجعل M, لان in uno sed male in marg. scr. Colv. corr. M الخبث E: ex لخبث 13

20 of Hippocrates Epidemics part I drier in hot, summery seasons because the moisture in the bodies of those suffering from it is reduced and depleted owing to the heat of these seasons. I 5 Hippocrates said [I 3: V 72,14 L.]: T h e fe r a l 1 and heartburn develop mostly in autumn. Galen said: Especially during the fruit season certain kinds of worms form in the belly as a result of the corruption of ingested fruit as well as other foods. There are three (kinds): one is thin, occurs around the anus and resembles the vinegar worm; another is thick and round, resembles a snake and occurs in the small intestine; and the last is wide, has a cut at the centre like a pumpkin seed and occurs in the large intestine. With his observation H i p p o c r a t e s wanted to subsume these three kinds under a single term and called them t h e fe r a l, that is, a savage animal. Some people said that he meant by t h e fe r a l elephantiasis because the G r e e k s named elephantiasis after the elephant and the elephant is a savage, voracious animal; also, elephantiasis occurs mostly in autumn. Others said that by t h e fe r a l he meant melancholy, not because this illness makes its victim physically resemble a beast as elephantiasis does, but psychologically and mentally. Yet others said that he meant by t h e fe r a l cancer because of the malignancy and seriousness of cancer. Yet others said that he meant 1 lit. wild or predatory

21 96 Galen, Commentary on the second book ضرورة ا ن يقع مثل هذا الاختلاف في الكلام الغامض ا ذ كان معنى صاحبه فيه ليس يوقف عليه وقوفا صحيحا. وا م ا وجع الفؤاد فقد ات فق عليه الجميع ا ن ه عرض يعرض في فم المعدة الذي قد كان القدماء يسم ونه باسم «الفؤاد» وهذا الوجع يكون بسبب الدود المتول د في 5 البطن ا ذا ارتفع فصار في هذه الناحية من المعدة ويكون ا يضا بسبب خلط رديء لذ اع وهو الخلط الذي يكون منه الدود المتول د في البطن. قال ا بقراط: وما كان من هذا فهو ا يضا ا قل ا فة من ا ن يكون المرض نفسه بهذه من الحال. قال جالينوس: يعني ا ن هذا الوجع العارض في الفؤاد متى كان في الوقت 10 المشاكل لحدوثه بمنزلة ما تقد م فوصفه كان ا قل ا فة من ا ن يكون بسبب المرض نفسه. وقد يوجد في بعض النسخ هذا الكلام على هذا المثال: «وما كان من هذين ا يضا فهو ا قل ا فة من ا ن يكون المرض نفسه بهذه من الحال» حت ى تفهم الا فة العارضة من العل تين اللتين ذكرهما وهما الدود ووجع الفؤاد. ومنفعة هذه الا قاويل كل ها هي نافعة في الاستدلال على سلامة الا مراض وخبثها. Ǧa-. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 142 v r 4. Ḥunayn, [وا م ا البطن 3 6 wāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r b. Maymūn, Fuṣūl IX [وهذا لذ اع : Medical Aphorisms II 79,2sq. (Ar.) Bos نفسه 9 11 [يعني. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 r v 1 E: من M 12 II الحدوثه E: لحدوثه E: om. M 10 من M 8 فهذا تفق E: فقد ات فق M 3 اذا E: ا ذ 1 om. M M: om. E كل ها هي 14

22 of Hippocrates Epidemics part I two or more of these things or all of them. This kind of dispute inevitably arises over an obscure passage since its author's meaning cannot be determined with certainty. Everyone on the other hand has agreed that h e a r t b u r n 1 is a symptom that occurs at the mouth of the stomach, which the ancients called heart, and that this pain occurs when the worms that form in the belly rise up and move to this region of the stomach. It is also caused by a bad, acrid humour; this is the humour that generates the worms that form in the belly. I 6 Hippocrates said [I 3: V 72,14 16 L.]: W hat is caused by this is also less harmful than when the disease itself is in this condition. Galen said: He means that when the pain that occurs in the heart arises in a season in which it regularly occurs, like what he described before, it is less harmful than when it occurs as a result of the disease itself. In some copies this passage appears as follows: what is caused by these two is also less harmful than when the disease itself is in this condition, so that the harm that occurs is understood to be caused by both diseases he mentioned, namely worms and heartburn. The benefit of all these remarks is that they are useful for determining whether diseases are benign or malignant. 1 lit. heart pain

23 98 Galen, Commentary on the second book 161 قال ا بقراط: وحال الدود ا يضا الصغير الذي يكون في ا سفل الا معاء بالعشي شبيهة بالحال في هذا وفي ذلك الوقت من اليوم يؤذي ذلك ا يضا في ا كثر الا مر لا من قبل ا ن ه يوجد الوجع ا زيد فقط ولكن بسببه خاص ة ا يضا. قال جالينوس: يريد ا ن حال وقت «العشي «والمساء من اليوم كل ه مثل حال 5 الخريف من السنة كل ها وذلك ا ن وقت الغداة شبيه بالربيع والوقت الذي بعده شبيه بالصيف ووقت العشي كما قلت قبل شبيه بالخريف ووقت الليل شبيه بالشتاء. فحركة «الدود بالعشي «في قوله شبيهة بما تقد م والذي تقد م هو ا ن الدود ا كثر ما يتحر ك في الخريف. وا م ا قوله في ا خر الكلام «لا من قبل ا ن ه يوجد الوجع ا زيد لكن بسببه خاص ة 10 ا يضا «فمعناه فيه ما ا صف: يقول ا ن هذا الدود في ذلك الوقت من اليوم يكون ا كثر ذلك لا من قبل ا ن ا بدان الناس تجد الا وجاع في ذلك الوقت ا زيد فقط ولكن من قبل ا ن الدود نفسه ا يضا من شا نه في طبيعته ا ن يتحر ك في ذلك الوقت. 5sq. بالشتاء [وقت v. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 143 r 4 6. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 2sq.. b. Maymūn, Fuṣūl V III 70: Medical Aphorisms II 57,1sq. (Ar.) Bos 7sq. الخريف [فحركة. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 4sq. الوقت [هذا. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 6sq. A 4 لكں M: لاكن E: ولكن E A: om. M فقط E A: om. M 3 ا يضا E M شبيه A: شبيهة 2 II حال M: ex هذا corr. وقت E 2 5 M b. Riḍwān Ḥunayn: om. E, in marg. add. قلت E 2 6 E: قل ن ا M E: om. M ا ن E 12 شبيه M: شبيهة M: om. E في قوله E: om. M 7 قبل

24 of Hippocrates Epidemics part I I 7 Hippocrates said [I 3: V 72,16 18 L.]: T h e c o n d i t i o n o f s m a l l wo r m s in the lower intestines in the evening also resembles this, and they are also troublesome mostly at that time of day, not just because the pain is greater (then), but particularly also because of themselves. Galen said: He means that the condition in the early and late e v e n i n g of the day as a whole resembles that in autumn of the year as a whole because morning resembles spring, the time after it resembles summer, evening, as I have said before, resembles autumn and night resembles winter. Hence, the movement of the w o r m s i n the evening in his remark corresponds to what has come before, namely that the worms move around mostly in autumn. The meaning of his words at the end of the passage, n o t j u s t b e c a u s e t h e pain is greater (then), but particularly also because of thems e l v e s, is as I shall describe: he says that these worms are more (painful) at that time of day not just because people's bodies feel pain more strongly at that time, but also because it is a natural characteristic of the worms themselves to move around at that time.

25 100 Galen, Commentary on the second book قال ا بقراط: ا حد ما يكون الا مراض وا قتلها في الخريف وذلك شبيه بهيجانها بالعشي في ا كثر الا مر لا ن للسنة دورا من الا مراض مثل ما لليوم دور من المرض. قال جالينوس: قد قيل معنى هذا الكلام فيما تقد م وهو ا ن ا بقراط يريد ا ن بين السنة وبين اليوم مناسبة. وا عني «باليوم» في كلامي هذا الزمان الذي بين طلوع 5 الشمس وبين غروبها لا كل الزمان الذي منذ طلوعها ا لى ا ن تعود فتطلع وقد س م ي ذلك «يوما وليلة». قال ا بقراط: الحال في كل واحد من ا مزجة الهواء بعضها عند بعض شبيهة بالحال في هيجان المرض بالعشي ما لم يتجد د شيء في الطبيعة العليا فا ن ه ا ن كان ذلك كان هذا ابتداء حال ا خرى فيجب ا ن تكون السنة بقياس نفسها على 10 هذا المثال. 162 قال جالينوس: ا م ا معنى هذا الكلام فليس بالغامض وذلك بسبب ما قيل فيما تقد م ا ل ا ا ن ي ا ظن ا ن الا لفاظ قد وقع فيها خطاء. فا ن ه ا ن ما يريد ا ن حال الخريف في «مزاج الهواء» في كل واحدة من السنين شبيهة بحال كل واحد من الا مراض 1sq. 6sq.. b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 143 r [ا حد بالعشي. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 8sq.. b. Maymūn, Fuṣūl VIII 70: Medical Aphorisms II 57,2sq. (Ar.) Bos L.: Hipp. Aphor. III 9: p. 401,7sq. Magdelaine = IV 488,16sq. [ا حد الخريف 1. Buqrāṭ, Fuṣūl 21,10sq. خريفي ة ,3 [حال. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v in دورا M A, in alio دور M ليوم A: E لليوم E A السنه M: للسنة M A b. Riḍwān: om. E بالعشي marg. scr. Colv.: دورا باليوم E 4 M: اليو م E هذا الزمان E M: in الازمان,هذه ut vid., corr. E 2 واحد M 7 بطلع :E فتطلع E منه :M منذ E :M correxi لكن [لا كل M وغ ر وبها :E وبين غروبها 5 M A: واحدة ا م ا E 11 M: om. E, in textu add. فا ن ه E 2 12 E: وان ه واحدة M 13 E: واحد M II السنين من M: om. E, السنين شبيهة بحال كل واحد in marg. add. E 3

26 of Hippocrates Epidemics part I I 8 Hippocrates said [I 4: V 72,19 74,2 L.]: Diseases are most acute and most fatal in autumn, and this corresponds to (the fact that) they exacerbate mostly in the evening, because the year has a disease cycle just as the day has a disease cycle. Galen said: What this passage means has been said before, namely that H i p p o - c r a t e s proposes that there is a correspondence between the year and the day. I mean by day in my usage the time between sunrise and sunset, not the time from its rise until its next rise, which is called a day and a night. I 9 Hippocrates said [I 4: V 74,2 5 L.]: T h e c o n d i t i o n o f e a c h m i x t u r e of the air in relation to another resembles the condition of the exacerbation of a disease in the evening as long as nothing has changed in the upper nature. 1 If that is the case, it marks the beginning of another condition. Hence, the year must relate to itself in the following manner: Galen said: The meaning of this passage is not obscure because of what was said before, but I think an error has occurred in the wording. He means that the condition of autumn each year with respect to the m i x t u r e o f t h e a i r resembles the condition of each disease with respect to its exacerbation in the evening, and that 1 The phrase in the upper nature (fī l-ṭabīʿati l-ʿulyā) translates ἐν τῷ ἄνω εἴδει (V 74,4 L.).

27 102 Galen, Commentary on the second book في «هيجانه بالعشي «وذلك يكون ا ذا حفظت السنة مزاجها على نظامه في ا وقاتها. فقد قال في كتاب الفصول: «متى كان في ا ي وقت من ا وقات السنة في يوم واحد مر ة حر ومر ة برد فتوق ع حدوث ا مراض خريفي ة». والا شياء التي «تتجد د في الطبيعة العليا» يعني في الهواء المحيط بالا بدان هي ا مور مزاجه كما دل في ا و ل 5 هذه المقالة فيما ذكر من ا مر الجمر الذي حدث بقرانون. قال ا بقراط: ا ذا كانت ا وقات السنة لازمة لنظامها وكان في كل وقت منها ما ينبغي ا ن يكون فيه كان ما يحدث فيها من الا مراض حسن النظام حسن البحران. وا ذا كانت ا وقات السنة غير لازمة لنظامها كان ما يحدث فيها من الا مراض غير منتظم سمج البحران من ذلك ما يكون بمدينة بارنثس متى نقص شيء ا و زاد فيها 10 ا م ا من الرياح وا م ا من عدمها وا م ا من المطر وا م ا من عدمه وا م ا من الحر وا م ا من البرد ثم يكون الربيع في ا كثر الا مر على ا فضل حالات الصح ة وا قل ما يحدث الموت. قال جالينوس: ا م ا الجزء الا و ل من هذا الكلام فقد قاله ا بقراط بهذا اللفظ في كتاب الفصول ا ل ا ا ن ه في هذه المقالة ا ضاف ا ليه شاهدا محق قا من مثال وصفه 15 وهو قوله «من ذلك ما يكون بمدينة بارنثس متى نقص شيء ا و زاد فيها» من 2sq. خريفي ة [متى Hipp. Aphor. III 4: p. 399,8sq. Magdelaine = IV 486,11 13 L.: v. Buqrāṭ, Fuṣūl 20,4sq. Buqrāṭ, Fuṣūl 21,5 10. Hipp. Aphor. III 8: p. 401,4 6 Magdelaine = IV 488,13 15 L.: [ا ذا البحران 6 9 fol.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., [وا ذا البرد v sq. الموت [ثم. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 18 11sq. الموت [يكون Hipp. Aphor. III 9: p. 401,8 Magdelaine = IV 488,17 L.:. Buqrāṭ, Fuṣūl 21,12 M, بارينس A: sine punctis E [بارنثس E A: om. M 9 كان E 8 بقرابيون M: بقرانون M ذكره E: ذكر 5 وقل Ḥunayn: E A وا قل M وثم A: E ثم M 11 ازداد A: E زاد Perinthus in marg. scr. Colv.: scripsi [بارنثس M: correxi 15 شيا ه دا E: شىا هد ا [شاهدا E اليها M: ا ليه M 14 وقد E: فقد M 13 Colv. in marg. add. او انقص M, شيء E: نقص شيء M: scripsi بارينس E: ٮارسس

28 of Hippocrates Epidemics part I this is the case when the year has kept its mixture in proper order during its seasons. He said in the Aphorisms: When it is in any season during the same day hot at one time and cold at another, expect the occurrence of autumnal diseases. The things which c h a n g e i n t h e u p p e r n a t u r e, that is, in the air surrounding bodies, are the specifics of its mixture, as he indicated at the beginning of this book when he discussed the carbuncles that occurred in C r a n o n. I 10 Hippocrates said [I 5: V 74,6 11 L.]: W h e n t h e s e a s o n s fo l l o w t h e i r (proper) order and things are as they should be during each of them, diseases that occur during them are regular and have a good crisis. W hen the seasons do not follow their (proper) order, diseases that occur during them are irregular and hard to bring to a crisis, for example in the city of Perinthus when there was during them some decrease or increase of wind or its absence, rain or its absence, heat or cold. Spring then is usually very healthy and least fatal. Galen said: H i p p o c r a t e s wrote the first part of this passage with the same words in the Aphorisms, but in this book he added corroborating evidence from a case he instances, namely his words fo r e x a m p l e w h e n i n t h e c i t y o f P e r i n - thus there was during them some decrease or increase of the things

29 104 Galen, Commentary on the second book الا شياء التي وصفها من ا ن الا مراض لا تبقى عند ذلك منتظمة فقد ينبغي ا ن تفهم هذا مضافا ا لى قوله. وا م ا قوله «وثم يكون الربيع على ا فضل حالات الصح ة وا قل ما يحدث الموت» فقد يمكن ا ن تفهم «في الربيع» نفسه فقط كا ن ه قال: «ا ن الربيع ا ن ما صار ا صح 5 الا وقات لا ن ه ليس تحدث فيه تغايير عظيمة كما تحدث في الخريف» ا ل ا ا ن هذا المعنى ليس بالمشاكل ل ما قصد له في هذا الكلام كل ه. ولذلك ا قول ا ن الا جود ا ن هذا القول ا ن ما هو شهادة مصح حة للقول الكل ي الذي تقد م من قول جزئي. وقوله «وثم «يحتمل في لسان اليوناني ين ا ن يكون معناه «من ث م «ا ي «من قبل ذلك» ويحتمل ا ن يكون معناه «هناك» فهو على المعنى الا و ل يقوم مقام «من 10 قبل» وعلى هذا المعنى الثاني يقوم مقام «هناك» حت ى يكون قوله كل ه في هذا 163 الموضع على هذا المثال: «من ذلك ما يكون بمدينة بارنثس متى نقص شيء ا و زاد» فسد نظام الا مراض الجاري في العادة على ا ن ذلك البلد ا عني بارنثس من ا صح البلدان ومن ا عظم ما يستدل به على ذلك ا ن الربيع فيه «على ا فضل حالات الصح ة». 15 وقد حذف قوم من هذا الكلام قوله «وا قل ما» على ا ن ه قد يوجد في جميع النسخ القديمة وقالوا ا ن قوله «وثم يكون الربيع على ا فضل حالات الصح ة» كلام داخل في الوسط فا ذا عزل كان ات صال الكلام على هذا المثال: «من ذلك ما 1 post تفهم add. هذا مما قال الى قو له E وثم 3 M: ثم E, in وثم in textu corr. E 2 وا قل E: وقل M 4 E فكانه M: كا ن ه M تغاير E: تغايير 5 E وكذلك M: ولذلك 6 7 in الطلي M, in uno الع لي E: الكل ي alio الٯ لي in marg. scr. Colv. اليونانين [اليوناني ين 8 E M: correxi معناه M: معنى E هناك 9 M: E هذاك Colv. in marg. scr. قبل in al من قبل 9sq. E فهو M: حت ى يكون 10 M: om. E هذا 11 :M correxi ان ما :E ان [ما :M scripsi بارينس :E ٮارٮٯس [بارنثس :M بارنس :E ٮارسس [بارنثس 12 correxi واقلها [وا قل ما 15 E M, scribendum وقل ما in marg. scr. Colv.: correxi 17 post ذلك add. E ان

30 of Hippocrates Epidemics part I that are the reason why, as he described, diseases do not remain regular. You need to understand this as an addition to his words. In his words spring then is usually very healthy and least fatal you could understand spring just by itself as if he had said: spring was the healthiest season because, unlike autumn, no great changes took place during it, but this interpretation does not agree with what he meant by this passage as a whole. I therefore say that the best (interpretation) is that these words are only substantiating evidence from a particular observation for the previous general statement. His expression t h e n in Greek can mean therefore, that is, because of that, but also there is. According to the first meaning it stands for because of, and according to this second meaning it stands for there is, so that on the whole he says the following at this point: for example when in the city of Perinthus there was some decrease or increase, it spoiled the regular course diseases normally take, even though that place, that is, Perinthus, is one of the healthiest places, and one of the most significant indicators for this is that spring is v e r y h e a l - t hy there. Some people omitted the phrase a n d l e a s t from this passage, even though it is found in all old copies, and said that his words s p r i n g t h e n i s u s u a l l y v e r y h e a l t h y got into the middle, and when they are removed, the text links up as fol-

31 106 Galen, Commentary on the second book يكون بمدينة بارنثس متى نقص شيء ا و زاد يحدث الموت على ا ن الربيع هناك على ا فضل حالات الصح ة». قال ا بقراط: ينبغي ا ن تتفق د الا مراض في ا وائلها هل تبلغ منتهاها سريعا وذلك يتبي ن من تزي دها وتزي دها ي عرف من ا دوارها وا مر البحران ا يضا من ذلك ي عرف. 5 قال جالينوس: قد وقع في ا و ل هذا الكلام بين النسخ اختلاف ا ل ا ا ن معناه وا ن كان الكلام مختلفا معنى واحد والجميع مت فق عليه وهو ا ن ا بقراط يتقد م ا ليك ا ن يكون ا هم الا شياء ا ليك ا ن تتفق د وتنظر منذ ا و ل الا مراض ا مر «منتهاها» متى يكون. فا ن ا بقراط قال في كتابه في تدبير الا مراض الحاد ة: «ا ن ما يقدر تدبير المريض كل ه بالنظر في هذا الباب» ا عني في منتهى المرض متى يكون وقال: «ا ن 10 ذلك ينفع في تدبير الا مراض ومن منتهى المرض يعرف ا مر بحرانه ا يضا». وقد بحثت عن هذا القول بحثا شافيا واستقصيته عن ا خره في كتابي في البحران وا نا واصف لك في هذا الموضع جملته وهي ا ن البحران التام لا يكون في وقت من الا وقات قبل منتهى المرض كما بي نت في ذلك الكتاب. ولذلك يجب ضرورة على من ا راد ا ن يعلم متى يكون هذا البحران ا ن يرتاض في تقدمة المعرفة 15 بمنتهى المرض. وقد بي ن ا بقراط ذلك في كتابه في تدبير الا مراض الحاد ة وا ن 3sq. تزي دها [ينبغي. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 20 ينبغي 3sq b. Riḍwān, Fawāʾid II 1: Cantabr. Dd , fol. 143 r [ا دوارها 7sq. يكون [ا هم. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 18sq. 8sq. الباب [ا ن ما non reperitur in Hipp. De diaeta acut. et in Buqrāṭ, Tadbīr 9sq. ا يضا [ا ن non reperitur in Hipp. De diaeta acut. et in Buqrāṭ, Tadbīr fol.. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., [ومن ا يضا v 20sq. 12sq. المرض II [البحران. Ḥunayn, Ǧawāmiʿ II 1: Ambrosianus B 135 sup., fol. 119 v 21 M فيه add. وتنظر M: om. E, in marg. add. E 2 7 post الكلام M: scripsi 6 بارينس E: ٮارسس [بارنثس 1 Colv. in marg. scr. شافيا M, in al شديد ا E: شافيا E 11 ىع رف M: ينفع E: om. M 10 قال 8 M واستقص يت :E واستقصيته M للذي :E لك في 12

32 of Hippocrates Epidemics part I lows: for example in the city of Perinthus when there was some decrease or increase, death occurred, even though spring is very healthy there. I 11 Hippocrates said [I 6: V 74,12 14 L.]: Yo u m u s t i nv e s t i g a t e a t t h e i r onset whether diseases reach their climax quickly. This is shown by their increase, and their increase is known from their cycles, as is the crisis. Galen said: The copies differ somewhat at the beginning of this passage, but although the text differs, the meaning is the same and everyone agrees on it, namely that H i p p o c r a t e s advises you that the most important thing for you is to investigate and examine at the beginning of diseases when their c l i m a x takes place. H i p - p o c r a t e s said in his book On Regimen in Acute Diseases: the treatment of a disease as a whole is possible only by examining this factor, namely when the climax of the disease takes place, and he said: this is useful in treating diseases, and from the climax of the disease the crisis is also known. I have sufficiently studied this passage and fully examined it in my book On the Crisis. 1 I shall summarise it for you at this point: there is no complete crisis at any time before the climax of a disease, as I have explained in that book, and it is therefore absolutely essential for anyone who wants to know when this crisis will occur to practise predicting the climax of the disease. H i p p o c r a t e s explained this in his book On 1 Here and elsewhere, the Arabic translation renders the title of De cris. as singular. The passage Galen alludes to is Gal. De cris. III 5: p. 181,5 185,3 Alexanderson = IX 724,8 729,18 K.

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

GALEN COMMENTARY ON T HE FIRST BOOK OF HIPPOCRATES' EPIDEMICS. Unauthenticated Download Date 6/15/18 1:53 PM

GALEN COMMENTARY ON T HE FIRST BOOK OF HIPPOCRATES' EPIDEMICS. Unauthenticated Download Date 6/15/18 1:53 PM شرح جالينوس للمقالة الا ولى من كتاب ا بقراط المسم ى ا فيذيميا GALEN COMMENTARY ON T HE FIRST BOOK OF HIPPOCRATES' EPIDEMICS CONSPECT VS SIGLORV M ET COMPENDIORV M A = codex Ayasofya 3642; s. XIV E = Scorialensis

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

Every set of first-order formulas is equivalent to an independent set

Every set of first-order formulas is equivalent to an independent set Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

Συντακτικές λειτουργίες

Συντακτικές λειτουργίες 2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.

Διαβάστε περισσότερα

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014 LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV 18 February 2014 Slowly/quietly Clear/clearly Clean Quickly/quick/fast Hurry (in a hurry) Driver Attention/caution/notice/care Dance Σιγά Καθαρά Καθαρός/η/ο

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

Math221: HW# 1 solutions

Math221: HW# 1 solutions Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin

Διαβάστε περισσότερα

Finite Field Problems: Solutions

Finite Field Problems: Solutions Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

Συστήματα Διαχείρισης Βάσεων Δεδομένων

Συστήματα Διαχείρισης Βάσεων Δεδομένων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Συστήματα Διαχείρισης Βάσεων Δεδομένων Φροντιστήριο 9: Transactions - part 1 Δημήτρης Πλεξουσάκης Τμήμα Επιστήμης Υπολογιστών Tutorial on Undo, Redo and Undo/Redo

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης Α.Τ.Ε.Ι. ΙΟΝΙΩΝ ΝΗΣΩΝ ΠΑΡΑΡΤΗΜΑ ΑΡΓΟΣΤΟΛΙΟΥ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Η διαμόρφωση επικοινωνιακής στρατηγικής (και των τακτικών ενεργειών) για την ενδυνάμωση της εταιρικής

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 11: The Unreal Past Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

14 Lesson 2: The Omega Verb - Present Tense

14 Lesson 2: The Omega Verb - Present Tense Lesson 2: The Omega Verb - Present Tense Day one I. Word Study and Grammar 1. Most Greek verbs end in in the first person singular. 2. The present tense is formed by adding endings to the present stem.

Διαβάστε περισσότερα

حديد. 5 ا فيذيميا. شرح جالينوس. E: اقايله يستنكر M 10 E: يسكر M, in al ىسىىكر in marg. scr. Colv. 11sq. حديد [ا لثغ hic post

حديد. 5 ا فيذيميا. شرح جالينوس. E: اقايله يستنكر M 10 E: يسكر M, in al ىسىىكر in marg. scr. Colv. 11sq. حديد [ا لثغ hic post شرح جالينوس للمقالة الثانية من كتاب ا بقراط المسم ى ا فيذيميا المقالة السادسة المقالة السادسة من تفسير جالينوس للمقالة الثانية من كتاب ا بقراط المسم ى 354 5 ا فيذيميا. قال جالينوس: ا ن هذه المقالة ا خر

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΝΟΜΙΚΟ ΚΑΙ ΘΕΣΜΙΚΟ ΦΟΡΟΛΟΓΙΚΟ ΠΛΑΙΣΙΟ ΚΤΗΣΗΣ ΚΑΙ ΕΚΜΕΤΑΛΛΕΥΣΗΣ ΠΛΟΙΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που υποβλήθηκε στο

Διαβάστε περισσότερα

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ Νικόλας Χριστοδούλου Λευκωσία, 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 1: Elements of Syntactic Structure Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * *

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * In the first chapter, we practiced the skill of reading Greek words. Now we want to try to understand some parts of what we read. There are a

Διαβάστε περισσότερα

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015 Adjectives Describing the Qualities of Things A lesson for the Paideia web-app Ian W. Scott, 2015 Getting Started with Adjectives It's hard to say much using only nouns and pronouns Simon is a father.

Διαβάστε περισσότερα

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014 LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV 4 February 2014 Somewhere κάπου (kapoo) Nowhere πουθενά (poothena) Elsewhere αλλού (aloo) Drawer το συρτάρι (sirtari) Page η σελίδα (selida) News τα νέα (nea)

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

Example Sheet 3 Solutions

Example Sheet 3 Solutions Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS ΟΜΗΡΟΥ ΙΛΙΑΔΑ ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS www.scooltime.gr [- 2 -] The Project Gutenberg EBook of Iliad, by Homer This ebook is for the use of anyone anywhere at no cost and with almost no restrictions

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

PARTIAL NOTES for 6.1 Trigonometric Identities

PARTIAL NOTES for 6.1 Trigonometric Identities PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live.

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live. Topic 1: Describe yourself Write your name, your nationality, your hobby, your pet. Write where you live. Χρησιμοποίησε το and. WRITE your paragraph in 40-60 words... 1 Topic 2: Describe your room Χρησιμοποίησε

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 4: English a Language of Economy Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

Διαβάστε περισσότερα

Srednicki Chapter 55

Srednicki Chapter 55 Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third

Διαβάστε περισσότερα

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ Ενότητα 1β: Principles of PS Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης

Διαβάστε περισσότερα

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

6.3 Forecasting ARMA processes

6.3 Forecasting ARMA processes 122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ» I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ

Διαβάστε περισσότερα

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple A/ Ονόματα και ένα παράδειγμα 1 Present Simple 7 Present PERFECT Simple 2 Present Continuous 8 Present PERFECT Continuous 3 Past Simple (+ used to) 9 Past PERFECT Simple she eats she is eating she ate

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα

Other Test Constructions: Likelihood Ratio & Bayes Tests

Other Test Constructions: Likelihood Ratio & Bayes Tests Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :

Διαβάστε περισσότερα

The challenges of non-stable predicates

The challenges of non-stable predicates The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates

Διαβάστε περισσότερα

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =? Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least

Διαβάστε περισσότερα

Μηχανική Μάθηση Hypothesis Testing

Μηχανική Μάθηση Hypothesis Testing ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider

Διαβάστε περισσότερα

"ΦΟΡΟΛΟΓΙΑ ΕΙΣΟΔΗΜΑΤΟΣ ΕΤΑΙΡΕΙΩΝ ΣΥΓΚΡΙΤΙΚΑ ΓΙΑ ΤΑ ΟΙΚΟΝΟΜΙΚΑ ΕΤΗ 2011-2013"

ΦΟΡΟΛΟΓΙΑ ΕΙΣΟΔΗΜΑΤΟΣ ΕΤΑΙΡΕΙΩΝ ΣΥΓΚΡΙΤΙΚΑ ΓΙΑ ΤΑ ΟΙΚΟΝΟΜΙΚΑ ΕΤΗ 2011-2013 ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΚΑΙ ΧΡΗΜΑΤΟΟΙΚΟΝΟΜΙΚΗΣ Επιμέλεια Κρανιωτάκη Δήμητρα Α.Μ. 8252 Κωστορρίζου Δήμητρα Α.Μ. 8206 Μελετίου Χαράλαμπος Α.Μ.

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal

Διαβάστε περισσότερα

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013 LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV 10 December 2013 I get up/i stand up I wash myself I shave myself I comb myself I dress myself Once (one time) Twice (two times) Three times Salary/wage/pay Alone/only

Διαβάστε περισσότερα

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE «ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing

Διαβάστε περισσότερα

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

Διαβάστε περισσότερα

ST5224: Advanced Statistical Theory II

ST5224: Advanced Statistical Theory II ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known

Διαβάστε περισσότερα

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ EΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΕΚΠΑΙΔΕΥΤΙΚΟ ΤΕΧΝΟΛΟΓΙΚΟ ΙΔΡΥΜΑ ΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : Λεωφ. Αντ.Τρίτση, Αργοστόλι Κεφαλληνίας Τ.Κ. 28 100 τηλ. : 26710-27311 fax : 26710-27312

Διαβάστε περισσότερα

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. Τα γνωστικά επίπεδα των επαγγελματιών υγείας Στην ανοσοποίηση κατά του ιού της γρίπης Σε δομές του νομού Λάρισας

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. Τα γνωστικά επίπεδα των επαγγελματιών υγείας Στην ανοσοποίηση κατά του ιού της γρίπης Σε δομές του νομού Λάρισας ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΜΗΜΑ ΙΑΤΡΙΚΗΣ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΩΤΟΒΑΘΜΙΑ ΦΡΟΝΤΙΔΑ ΥΓΕΙΑΣ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ Τα γνωστικά επίπεδα των επαγγελματιών υγείας Στην ανοσοποίηση

Διαβάστε περισσότερα

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α. Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:.

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α.  Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:. ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α 2 ειδήσεις από ελληνικές εφημερίδες: 1. Τα Νέα, 13-4-2010, Σε ανθρώπινο λάθος αποδίδουν τη συντριβή του αεροσκάφους, http://www.tanea.gr/default.asp?pid=2&artid=4569526&ct=2 2. Τα Νέα,

Διαβάστε περισσότερα

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής Ενότητα 12b: The Little Prince Τμήμα Εφαρμοσμένης Πληροφορικής Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που υπόκειται

Διαβάστε περισσότερα

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα. Ξενόγλωσση Τεχνική Ορολογία

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα. Ξενόγλωσση Τεχνική Ορολογία ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Ξενόγλωσση Τεχνική Ορολογία Ενότητα: Principles of an Internal Combustion Engine Παναγιώτης Τσατσαρός Τμήμα Μηχανολόγων Μηχανικών

Διαβάστε περισσότερα

Chapter 29. Adjectival Participle

Chapter 29. Adjectival Participle Chapter 29 Adjectival Participle Overview (29.3-5) Definition: Verbal adjective Function: they may function adverbially or adjectivally Forms: No new forms because adverbial and adjectival participles

Διαβάστε περισσότερα

Εγχειρίδια Μαθηµατικών και Χταποδάκι στα Κάρβουνα

Εγχειρίδια Μαθηµατικών και Χταποδάκι στα Κάρβουνα [ 1 ] Πανεπιστήµιο Κύπρου Εγχειρίδια Μαθηµατικών και Χταποδάκι στα Κάρβουνα Νίκος Στυλιανόπουλος, Πανεπιστήµιο Κύπρου Λευκωσία, εκέµβριος 2009 [ 2 ] Πανεπιστήµιο Κύπρου Πόσο σηµαντική είναι η απόδειξη

Διαβάστε περισσότερα

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

Διαβάστε περισσότερα

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Δρ. Παναγιώτης Πεντάρης - University of Greenwich - Association for the Study of Death and Society (ASDS) Περιεχόµενα Εννοιολογικές

Διαβάστε περισσότερα

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014 LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26 18 November 2014 But Weekend I love The song I sing I smile I laugh Greek (thing) Greek(people) Greek (man) αλλά (το) Σαββατοκύριακο αγαπώ (το) τραγούδι τραγουδώ

Διαβάστε περισσότερα

1) Formulation of the Problem as a Linear Programming Model

1) Formulation of the Problem as a Linear Programming Model 1) Formulation of the Problem as a Linear Programming Model Let xi = the amount of money invested in each of the potential investments in, where (i=1,2, ) x1 = the amount of money invested in Savings Account

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

Block Ciphers Modes. Ramki Thurimella

Block Ciphers Modes. Ramki Thurimella Block Ciphers Modes Ramki Thurimella Only Encryption I.e. messages could be modified Should not assume that nonsensical messages do no harm Always must be combined with authentication 2 Padding Must be

Διαβάστε περισσότερα

Living and Nonliving Created by: Maria Okraska

Living and Nonliving Created by: Maria Okraska Living and Nonliving Created by: Maria Okraska http://enchantingclassroom.blogspot.com Living Living things grow, change, and reproduce. They need air, water, food, and a place to live in order to survive.

Διαβάστε περισσότερα

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics Fourier Series MATH 211, Calculus II J. Robert Buchanan Department of Mathematics Spring 2018 Introduction Not all functions can be represented by Taylor series. f (k) (c) A Taylor series f (x) = (x c)

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

ΑΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΑΡΓΟΣΤΟΛΙ ΚΕΦΑΛΗΝΙΑΣ

ΑΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΑΡΓΟΣΤΟΛΙ ΚΕΦΑΛΗΝΙΑΣ ΑΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΑΡΓΟΣΤΟΛΙ ΚΕΦΑΛΗΝΙΑΣ 2014 Η ΜΕΤΑΒΑΣΗ ΑΠΟ ΤΗ ΣΤΑΘΕΡΗ ΣΤΗ ΚΙΝΗΤΗ ΤΗΛΕΦΩΝΙΑ ΚΑΙ ΟΙ ΕΠΙΔΡΑΣΕΙΣ ΤΗΣ ΣΤΗΝ ΕΠΙΚΟΙΝΩΝΙΑΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΕΠΙΒΛΕΠΩΝ ΚΑΘΗΓΗΤΗΣ:

Διαβάστε περισσότερα

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.

Διαβάστε περισσότερα

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Business English Ενότητα # 9: Financial Planning Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων Άδειες Χρήσης Το παρόν εκπαιδευτικό

Διαβάστε περισσότερα

Door Hinge replacement (Rear Left Door)

Door Hinge replacement (Rear Left Door) Door Hinge replacement (Rear Left Door) We will continue the previous article by replacing the hinges of the rear left hand side door. I will use again the same procedure and means I employed during the

Διαβάστε περισσότερα

Calculating the propagation delay of coaxial cable

Calculating the propagation delay of coaxial cable Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric

Διαβάστε περισσότερα

Μετρήσεις ηλιοφάνειας στην Κύπρο

Μετρήσεις ηλιοφάνειας στην Κύπρο Πτυχιακή εργασία Μετρήσεις ηλιοφάνειας στην Κύπρο Ιωσήφ Μικαίος Λεμεσός, Μάιος 2018 1 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΓΕΩΤΕΧΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΑΧΕΙΡΙΣΗΣ ΠΕΡΙΒΑΛΛΟΝΤΟΣ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ

Διαβάστε περισσότερα

ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω

ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω 0 1 2 3 4 5 6 ω ω + 1 ω + 2 ω + 3 ω + 4 ω2 ω2 + 1 ω2 + 2 ω2 + 3 ω3 ω3 + 1 ω3 + 2 ω4 ω4 + 1 ω5 ω 2 ω 2 + 1 ω 2 + 2 ω 2 + ω ω 2 + ω + 1 ω 2 + ω2 ω 2 2 ω 2 2 + 1 ω 2 2 + ω ω 2 3 ω 3 ω 3 + 1 ω 3 + ω ω 3 +

Διαβάστε περισσότερα

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1. Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given

Διαβάστε περισσότερα