| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one respectively equal to the three sides of the other, each to each, the triangles are equal, and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA, if AB, BC,... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...triangle is equilateral. PROP. VII. THEOR. If two triangles have three sides of the one re-spectively equal to the three sides of the other, each to each, the triangles are equal, and the angles are equal which are opposite to the equal sides. In ^s CBA, CDA, if AB, BC,... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...AP, since PB = PC, the oblique line AB = AC (B. VI, Prop, v) ; therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other ; consequently they are equal (BI, Prop, vm), and the angle ADB is equal to ADC ; therefore each is... | |
| Elias Loomis - Conic sections - 1849 - 252 pages
...equal, each to each, and the triangles themselves will be equal. Let ABC, DBF be two triangles having the three sides of the one equal to the three sides of the other, viz.: AB equal to DE, BC to EF, and AC to DF ; then will the three angles also be equal, viz.: the... | |
| Charles Davies - Logic - 1850 - 398 pages
...proposition, we need the following, which have been before proved ; viz. : Prop. X. (of Legendre). "When two triangles have the three sides of the one equal...to the three sides of the other, each to each, the three angles will also be equal, each to each, and the triangles themselves will be equal." Prop. V.... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...AP, since PB = PC, the oblique line AB = AC, (B. VI, Prop. v;) therefore the two triangles ADB, ADC have the three sides of the one equal to the three sides of the other; consequently they are equal, (B. I, Prop, viu,) and the angle ADB is equal to ADC ; therefore each... | |
| Charles Davies - Geometry - 1850 - 218 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note. When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
| Charles Davies - Geometry - 1850 - 238 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, have the three sides of the one equal to the three sides of the Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...these results contradicts the hypothesis : therefore, BA C is greater than EDF. PROPOSITION X. THEOEEM. If two triangles have the three sides of the one equal...three sides of the other, each to each, the triangles are equal. Let EDF and BAC be two triangles, having the side ED=BA, the side EF^BC, and the side DF=AC;... | |
| Charles Davies - Geometry - 1886 - 340 pages
...EAD will be equal to tho angle K. For, draw the chord DE. Then the two triangles IKL and EAD, having the three sides of the one equal to the three sides of the other, each to each, the angle EAD will be equal to the angle K (Bk. I. Th. viii). PROBLEM 1X. Through a g1ven po1nt to draw... | |
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