| Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...are equal (Def. 4), therefore AD=DB (BI Prop. 19, Cor. 2); hence the two triangles ACD, BCD, having **the three sides of the one equal to the three sides of the other,** are equal, (B. I. Prop. 22), and the angles ACD, BCD, are equal ; and therefore the arcs AE, EB,are... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 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,... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 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,... | |
| George Roberts Perkins - Geometry - 1847 - 308 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 - 375 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...each, and the triangles themselves will be equal."** Prop. V. " When two triangles have two Propositio„ sides and the included angle of the one, equal... | |
| Charles Davies - Logic - 1850 - 390 pages
...Legendre). "When two triangles Previous have the three sides of the one equal to the three tmths^eces" **sides of the other, each to each, the .three angles...each, and the triangles themselves will be equal."** Prop. V. " When two triangles have two Proposition sides and the included angle of the one, equal to... | |
| Charles Davies - Logic - 1850 - 375 pages
...Legendre). " When two triangles p^.,,^ have the three sides of the one equal to the three lnah " """"' tides **of the other, each to each, the three angles will...each, and the triangles themselves will be equal."** Prop. V. " When two triangles have two tides and the included angle of the one, equal to two sides... | |
| 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... | |
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