 | 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... | |
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IF a straight line fall upon two parallel straight lines it makes 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 same side together... 
