 | Charles Hutton - 1811 - 404 σελίδες
...the elements of Geometry, vol. 1) that two spherical triangles are equal tor each other, 1 st. When the three sides of the one are respectively equal to the three sides of the other. 2dly. When each of them has an equal angle contained between equal sides: and, 3dly. When they have... | |
 | Charles Hutton - 1812 - 624 σελίδες
...in the elements of Geometry, vol. 1) that two spherical triangles are equal to each other, 1st. When the three sides of the one are respectively equal to the three sides of the other. 2Uly. When each of them has an equal angle contained between equal sides : and, 3dly. When lliey have... | |
 | Adrien Marie Legendre - 1822 - 394 σελίδες
...hypothesis; therefore, BAC is greater than EDF. PROPOSITION XI. THEOREM. Two triangles are equal, when the three sides of the one are respectively equal to the three sides of the other. LET the side AB (see the diagram of Prop. 6.) be equal to DE, AC=DF, BC=EF; then is the angle A=D,... | |
 | Charles Hutton - 1822 - 680 σελίδες
...of Geometry, vol. 1) that two spherical triangles are equal to each other, 1st. When the threesides of the one are respectively equal to the three sides of the other. 2dly. When each of them has an equal angle contained between equal sides : and, 3dly. When they have... | |
 | 1854 - 1112 σελίδες
...two triangles have the three angles in one respectively equal to the three in the other: (consequent) the three sides of the one are respectively equal to the three of the other ; which is incorrect. Proposition 6. — Problem. To bisect a given rectilineal angle... | |
 | Adrien Marie Legendre - 1828 - 346 σελίδες
...contradict the hypothesis ; therefore, BAC is greater than EDF. THEOREM. 43. Two triangles are equal, when the three sides of the one are respectively equal to the three sides of the other3TB Let the side AB=DE, = DF, BC = EF; then is the angle A=D, B=E, C=F. For, rt the angle A were... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...ED; .-. EF : EG=EF : ED ; hence EG=ED. (Lem., p. 116.) "Wherefore in the two triangles EDF and EOF, the three sides of the one are respectively equal to the three sides of the other ; .•. the angles are = that are opposite to the equal sides, (Prop. 9); that is, the /DEF = the Z.GEF,... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 σελίδες
...will be perpendicular to BC. 19. THEOREM. The triangles DEF and ABC are equal in all respects, when cr the three sides of the one are respectively equal to the three sides of the other, that is, = AB, = AC, PRINCIPLES OP GEOMETRY. Let DEP be placed below ABC, so that DE shall coincide... | |
 | Eli Todd Tappan - 1864 - 288 σελίδες
...enough, to determine the triangle. THREE SIDES EQUAL. 282. Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. Let the side BD be equal to AI, the side BC equal to AE, and CD to El ; then the two triangles are... | |
 | Richard Wormell - 1868 - 286 σελίδες
...included side of the one are respectively equal to the corresponding parts of the other. 3rd. When the three sides of the one are respectively equal to the three sides of the other. 12. Prove that when two sides of a triangle are respectively equal to two sides of another, but the... | |
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Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. 
