...ninety degrees. The ambiguity is avoided, if the fum of the other two angles be known ; becaufe [32. IJ the three angles of a triangle are together equal to two right angles. PROP. V. THEOR. Fig. 14. 5. The fum of any fwofides, BA.and AC, of any triangle ABC, is to the difference...

...perpendicular to another. A THEOREM, a fpeculative propof1tion, the truth of which may be demonftrated ; as the three angles of a triangle are together equal to two right angles, or 1 80 degrees. 46. A DEMONSTRAT1ON is the proof of the truth of any aflertion. 47. Though it be our...

...impoffible to draw any concluiion, with refpect to real objects : thus, when I have demonftrated that the three angles of a triangle are together equal to two right angles, this is a property belonging only to an abilract triangle, and not at all to one really exifting. But...

...independently of all consideration of parallel lines, that the three angles of a triangle are together cqual to two right angles, the object in view would be accomplished, and the difficulty, in this part of the elements, would be entirely overcome. Now, the theorem just mentioned would be easily demonstrated,...

...An exterior angle of a triangle is equal to both its opposite interior angles, and all the interior angles of a triangle are together equal to two right angles. The exterior angle BCD, formed by the production of the side AC of the triangle ABC, is equal to the two...

...confequence, till now, has ever been deduced. If we could demonftrate, independently of all confideration of parallel lines, that the three angles of a triangle...equal to two right angles, the object in view would be accomplifhed, and the difficulty, in this part of the Elements, would be entirely overcome. Now, the...

...draw DF parallel to CE, and ECDF will be the rectangle contained by A and B, as was required ". « The three angles of a triangle are together equal to two right angles (Enclid 38. 1.) that is, to 180°; wherefore if the sum of two angles of a triangle be subtracted from...

...was surely much to be condemned. Bossut's Elements of Geometry, which appeared about the year 1775, is almost the only one in the French language, except...would be accomplished, and the difficulty, in this part of the Elements, would be enVOL. iv. y tirely overcome. Now, the theorem just mentioned would...

...fundamental truths of the science of geometry. Among those analytical methods of demonstration, to winch an allusion is made above, we were long since particularly...would be accomplished, and the difficulty, in this part of the Elements, would be entirely overcome. Now, the theorem just mentioned would be easily demonstrated,...

...introduction of a proposition as an axiom, which certainly is by no means self-evident. Later writers haye uniformly experienced the same difficulty ; and some...angles, the object in view would be accomplished, arid the difficulty, in this part of the Elements, would be enVOL. iv. y tirely.overcome. Now, the...