| Education - 1868
...similarity to those of the other. " — Campbells Rhet. This structure is very often neglected. Examples : **"If two triangles have the three sides of the one...to the three sides of the other, each to each, the** triangles will be equal in all their parts." The article before one here is improper, because the reference... | |
| James Maurice Wilson - Geometry - 1868
...one triangle can be constructed so as to have its sides equal to three given lines, it is clear that **if two triangles have the three sides of the one equal to the three sides of the other,** these triangles must be identical, or be equal in all respects. And a similar remark may be made on... | |
| James Maurice Wilson - Geometry - 1868 - 150 pages
...are therefore equal. And if the chord AB is given equal to the chord PQ, then the triangles AOB, POQ **have the three sides of the one equal to the three sides of the other;** and therefore the angle AOB=\he angle POQ; and therefore also the arc AB = the arc PQ. COR. 1. If the... | |
| Benjamin Greenleaf - 1868 - 338 pages
...than ABC. PROPOSITION XVII. — THEOREM. ELEMENTS OP GEOMETRY. Let ABC, DBF be two triangles, having **the three sides of the one equal to the three sides of the other,** eaeh to each, namely, AB to DE, AC toDF, andCB toEF; then their triangles will be equivalent. Let 0... | |
| Bernhard Marks - Geometry - 1869 - 180 pages
...angle c, opposite the side A B. I) B PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, **If two triangles have the three sides of the one equal to the three sides of the other, each to each,** they are equal in all their parts. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Horatio Nelson Robinson - 1869 - 276 pages
...remain ED = CF, (Ax. 3); but BE = AC, and AF= BD, (Th. 24); hence we have two A's, CAF and EBD, which **have the three sides of the one equal to the three sides of the other, each to each;** therefore, the two A's are equal, (Th. 21). If, from the whole figure ABDC, we take away the A CAF,... | |
| Charles Davies - Geometry - 1870 - 319 pages
...called a direct, and the latter an indirect demonstration. THEOREM via. If two triangles have tlie **three sides of the one equal to the three sides of the other, each to each, the three angles will** aho be equal, each to each. Let the two triangles ABC, ABD, have the side AB equal to the side AB,... | |
| Euclides - 1871
...If two angles of a triangle be.equal, the sides wMch tubtend them are also equal. (Eucl. i. 6.) SE 2 **If two triangles have the three sides of the one equal...to the three sides of the other, each to each, the** triangles must be equal in all respects. -25 q _ Let the three sides of the A s ABO, DEF be equal,... | |
| Bernard Marks - Geometry - 1871 - 172 pages
...the side A B. THEOREMS ILLUSTRATED. PROPOSITION XIX. THEOREM. DEMONSTRATION. We wish to prove that, **If two triangles have the three sides of the one equal to the three sides of the other, each to each,** they are equal in all their part's. Let the two triangles ABC, ADC, have the side AB of the one equal... | |
| Euclid, Charles Peter MASON - Geometry - 1872
...likewise those terminating in the other extremity of the base equal to one another. PROPOSITION VIII. **If two triangles have the three sides of the one equal to the three sides of the other, each to each,** then the triangles will also be equal to each other in every other respect, that is, the angles of... | |
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