| 1858 - 398 pages
...alternate angles equal to one another ; and the exterior angle equal to the interior and opposite angle **upon the same side ; and likewise the two interior...the same side together equal to two right angles.** 3. PROP. XL VIII. — If the square described upon one t>f the sides of a triangle, be equal to the... | |
| Euclides - 1858 - 248 pages
...alternate angles equal to one another ; and the exterior angle equal to the interior and opposite angle **upon the same side ; and likewise the two interior angles upon the same side together equal to two** rt. angles. DEMONSTRATION. — Ax. 4. If equals be added to unequals, the wholes are unequal. P. 13.... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...exterior angle equal to the interior and opposite on the same side ; and the two interior angles on **the same side together equal to two right angles. Let the straight line EF** intersect E the two parallel lines AB, CD ; the \ alternate angles AGH, GHD are \Ct__---- equal to... | |
| Euclides - 1860 - 288 pages
...the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite **upon the same side ; and likewise the two interior...the same side together equal to two right angles.** Given the straight line EF falling upon the parallel straight lines AB, CD ; to prove that the alternate... | |
| Civil service - 366 pages
...alternate angles equal to one another ; and the exterior angle equal to the interior and opposite angle **upon the same side ; and likewise the two interior...the same side together equal to two right angles.** PKOP. XL VIII. — If the square described upon one of the sides of a triangle, be equal to the squares... | |
| Royal college of surgeons of England - 1860 - 336 pages
...the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite **upon the same side ; and likewise the two interior angles upon the** saine side together equal to two right angles. 6. Parallelograms upon the same base, and between the... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...the exterior angle equal to the interior and opposite upon the same side of the line ; or make the **interior angles upon the same side together equal to two right angles** ; the two straight lines shall be parallel to one another. Let the straight line EF, which falls upon... | |
| War office - 1861 - 260 pages
...alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on **the same side, and likewise the two interior angles...the same side together equal to two right angles.** 2. Draw a straight line from a given point without the circumference which shall touch a given circle.... | |
| Euclides - 1862 - 172 pages
...alternate angles equal to each other ; and the exterior angle equal to the interior and opposite angle **upon the same side; and likewise the two interior...the same side together equal to two right angles.** (References — Prop. i. 13, 15; ax. l. 2, 4, 12.) Let the right line EF, fall on the parallel lines... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the alternate angles equal; also any exterior angle equal to the interior and opposite angle ; and **the two interior angles upon the same side together...equal to two right angles. Let the straight line EF** inter- E sect the parallel lines AB, CD ; \ the alternate angles AGH, GHD Vj ____—•• — * are... | |
| |