 | Euclides - 1838 - 264 pages
...at A is equalt to the angle at D : wheretssPi. fore the remaining angle at C is equalt to the c«"i remaining angle at F : therefore the triangle ABC...triangle DEF. Next, let each of the angles at C, F be not less than a right angle : the triangle ABC shall also in this case be equiangular to the triangle DEF.... | |
 | Robert Simson - Geometry - 1838 - 434 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, &c. QED PROP. XXVIII. THEOR. IN equal circles, equal straight lines cut off equal... | |
 | Euclides - Geometry - 1841 - 378 pages
...at * 20. s. A is half* of the angle BGC, and the angle at D half * 7 Ax. 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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 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 be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.... | |
 | Euclides - 1842 - 316 pages
...the angle at A (20. 3.) 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... | |
 | John Playfair - Euclid's Elements - 1844 - 338 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...the triangle ABC is equiangular to the triangle DEF. wherefore (4. 6.), AB : BG :: DE : EF; but, by hypothesis, DE : EF :: AB : BC, therefore, AB : BC :... | |
 | Euclides - 1845 - 546 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 D : (hyp.) wherefore the remaining angle at C is equal to the remaining angle at F: (i. 32.) therefore... | |
 | Euclid - Geometry - 1845 - 218 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, &c. QED PROPOSITION XXVIII. THEOB. — In equal circles, equal straight lines cut... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 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...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 - 1846 - 292 pages
...the angle at A is half of the angle BGC, aad the angle at D half of the angle EHF ; therefore also the angle at A is equal to the angle at D. Wherefore, In equal circles §c. QED PROP. XXVIII. In equal circles, equal straight lines cut off equal circumferences,... | |
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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. 
