 | John Playfair - Euclid's Elements - 1847 - 340 pages
...than a right angle ; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal : And the angle at A is equal to the angle at...triangle DEF. Next, let each of the angles at C, F bo not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...it: And the angle at A is half of the angle BGC, and the angle at D half of the angle EHF : Therefore the angle at A is equal to the angle at D. Wherefore in equal circles, &c. QED PROP. XXVIII. THEOR. In equal circles, equal straight lines cut off" equal... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...: And the angle at A is half of the angle BGC, and the angle at D half of the angle EHF ; therefore the angle at A is equal to the angle at D. Wherefore, in equal circles, etc. QED PROPOSITION XXVIII. THEOR. In equal circles, equal straight lines cut off"... | |
 | Euclides - 1853 - 146 pages
...angle at A is half of the angle BGC, and the angle at D half of the angle EHF; therefore (Ax. 7.) 4. The angle at A is equal to the angle at D. Wherefore, in equal circles, &c. QED PROP. XXVIII. THEOREM. In equal circles, equal straight lines cut off equal... | |
 | Euclides - Geometry - 1853 - 176 pages
...it. And the angle at a is half of the angle bgС, and the angle at d half of the angle ehf: therefore the angle at a is equal to the angle at d. Wherefore, in equal circles, &c. QED PROPOSITION XXVIII. — THEOREM., In equal circles, equal straight lines... | |
 | Euclides - 1855 - 230 pages
...same manner it may be shown that the angle at E is not greater than the angle ABC; therefore they are equal, and the angle at A is equal to the angle at...remaining angle at C is equal to the remaining angle at F ; and the triangles ABC and DEF are equiangular, and therefore have the sides about the equal angles... | |
 | John Playfair - Geometry - 1855 - 334 pages
...than a right angle; which is absurd. Therefore the angles ABC, DEF are not unequal, that is, they are equal: And the angle at A is equal to the angle at...remaining angle at C is equal to the remaining angle atF; Therefore the triangle ABC is equiangular to the triangle DEF. wherefore (4. 6.), AB : BG :: DE... | |
 | Euclides - 1855 - 270 pages
...equal to the angle D EF (I. Ax. 1). For the same reason, the angle A С B is equal to the angle D FE, and the angle at A is equal to the angle at D. Therefore the triangle AB С is equiangular to the triangle DE F. Wherefore, if the sides, &e. QED... | |
 | John Playfair - Euclid's Elements - 1856 - 346 pages
...at A is equal to the angle at D ; wherefore the remaining angle at C is equal to the remaining anglo at F ; Therefore the triangle ABC is equiangular to...triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.... | |
 | Euclides - 1860 - 288 pages
...right angle, which is absurd ; therefore the angles ABC and DEF are not unequal ; that is, they are equal ; and the angle at A is equal to the angle at...the triangle DEF. Next, let each of the angles at C and F be given not less than a right angle ; to prove that the triangle ABC is also in this case equiangular... | |
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D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. 
