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Euclid: Elementa

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Click to Expand/Collapse OptionTitle
Click to Expand/Collapse OptionPreface
Click to Expand/Collapse OptionBook I
Click to Expand/Collapse OptionBook ΙI
Click to Expand/Collapse OptionBook IΙΙ
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gre I,18
ὅπερ ἔδει δεῖξαι.
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eng
Q. E. D.
lat Sic
Quod oportet (ostendere).
lat Gerard
Et hoc est quod demonstrare voluimus.
lat Adelard
Quod demonstrare intendimus.
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi p. 11-12
وذلك ما اردناه
اقول وان اخرجنا (ا ج) الى (د) وجعلنا (ا د) مثل (ا ب) [ج] ووصلنا (د ب) امكن (١٢) اثبات المطلوب بمثل البيان المذكور وبوجه آخر نرسم على مركز (ا) ببعد (ا ب) دائرة (ب د) ونخرج (ب ج) الى (د) ونصل (ا د) فزاوية (ا ج ب) الخارجة اعظم من زاوية (ا د ب) المساوية لزاوية (ا ب د) [ه]
ara Nairizi p. 86
وذلك ما اردنا ان نيبين
san 24,9-24
tad evam upapannam |
      punaḥ prakārāntaram |
   ajarekhā daparyantaṃ neyā | abatulyaṃ adaṃ ca kāryam | dabarekhā ca kāryā | tatra abadakoṇa adabakoṇau samānau staḥ | abadakoṇas tu abajakoṇān mahān asti | adabakoṇo ’pi abajakoṇān mahān asti | punaḥ ajabakoṇaḥ adabakoṇād adhiko ’sti | tasmāt ajabakoṇaḥ abajakoṇād atīva mahān jātaḥ | tad evopapannaṃ yathoktam ||
      punaḥ prakārāntaram |
   aṃ kendraṃ kṛtvā abavyāsārddhena badavṛttaṃ kāryam | bajarekhā vṛttalagnā daparyantaṃ neyā | adarekhā ca kāryā | abadatribhuje bakoṇadakoṇau samānau staḥ | ajabakoṇaś ca adabakoṇād adhikaḥ | abadakoṇād apy adhiko bhavati | idam eveṣṭam asmākam ||
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lat Clavius
Quod demonstrandum erat.

COROLLARIVM
EX hoc sequitur, omnes tres angulos trianguli Scaleni esse inæquales, ut monuimus defin. 15. huius lib. Sit enim triangulum Scalenum A B C, cuius maximum quidem latus A C, minimum autem B C, & medium locum habens A B. Dico eiusdem omnes angulos inæquales esse. Cum enim latus A C, ponatur maius latere A B, erit per hanc propositio angulus B, angulo C, maior. Eadem ratione maior erit angulus C, angulo A, quandoquidem & latus A B, latere B C, maius ponitur. Sunt igitur omnes tres anguli inæquales, maximus quidem B, minimus vero A, & C, medium locum inter utrumque tenens.
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