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Euclid: Elementa
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Proposition 17. 
THEOR. 10. PROPOS. 17. 
第十七題 
In any triangle two angles taken together in any manner are less than two right angles. 
CVIVSCVNQVE trianguli duo anguli duobus rectis sunt minores, omnifariam sumpti. 
凡三角形之每兩角。必小於兩直角。 
Let ABC be a triangle;  I say that two angles of the triangle ABC taken together in any manner are less than two right angles. 
Sit triangulum A B C;  Dico duos angulos A B C, & A C B, minores esse duobus rectis; Item duos C B A, & C A B; Itemque duos B A C, & B C A. 
.  . 
For let BC be produced to D. [Post. 2]  Then, since the angle ACD is an exterior angle of the triangle ABC, it is greater than the interior and opposite angle ABC. [I. 16]  Let the angle ACB be added to each;  therefore the angles ACD, ACB are greater than the angles ABC, BCA.  But the angles ACD, ACB are equal to two right angles. [I. 13]  Therefore the angles ABC, BCA are less than two right angles.  Similarly we can prove that the angles BAC, ACB are also less than two right angles, and so are the angles CAB, ABC as well. 
Producantur enim duo quæuis latera, nempe C B, C A, ad D, & E.   Quoniam igitur angulus A B D, externus maior est interno & opposio angulo A C B;  si addatur communis angulus A B C,   erunt duo anguli A B D, A B C, maiores duobus angulis A B C, A C B:  Sed A B D, A B C, æquales sunt duobus rectis.   Igitur A B C, A C B, minores sunt duobus rectis.   Eadem ratione erunt anguli C B A, & C A B, minores duobus rectis. Item duo B A C, & B C A. 
.  .  .  .  .  .  . 
Therefore etc.  Q. E. D. 
Cuiuscunque igitur trianguli, &c.   Quod erat demonstrandum.

EX PROCLO
HINC perspicuum est, ab eodem puncto ad eandem rectam lineam non posse deduci plures lineas perpendiculares, quam unam. Si enim fieri potest, ducantur ex A, ad rectam B C, duæ perpendiculares A B, A C. Erunt igitur in triangulo A B C, duo anguli interni B, & C, duobus rectis æquales, cum sint duo recti, quod est absurdum. Sunt enim quilibet duo anguli in triangulo quocunque ostensi minores duobus rectis. Non ergo plures perpendiculares, quam vna, ex A, ad B C, deduci possunt. Quod est propositum.

COROLLARIVM
CONSTAT etiam ex his, In omni triangulo, cuius unus angulus fuerit rectus, vel obtusus, reliquos esse acutos, ceu monuimus defin. 26. huius lib. Cum enim per hanc propositio duo quilibet anguli sint duobus rectis minores, necesse est, si unus fuerit rectus, vel obtusus, quemcunque reliquorum esse acutum, ne duos angulos in triangulo rectos, aut duobus rectis maiores esse fateamur. 
.  . 
 
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