| John Keill - Logarithms - 1723 - 364 pages
...are to each other a* -their Bafes; which was to be demonftrated. PROPOSITION II. THEOREM. If it Right **Line be drawn parallel to one of the Sides of a "Triangle, it** frail cut the Sides of the Triangle * proportionally ; and if the Sides of the Triangle be cut proportionally,... | |
| John Keill - Geometry - 1772 - 399 pages
...fameBafe, J are between the fame Parallels; therefoie DE is parallel to B C. Wherefore, if c Right Lint **be drawn parallel to one of the Sides of a Triangle, it** jhall cut the Si Jo of the Triangle proportionally ; and if the Sines cf the Triangle be cut proportionally,... | |
| Benjamin Donne - Mathematics - 1775 - 159 pages
...other Sides, or thefe Side* produced, proportionally, (viz. BD : DA :: CE : EA, or AB : AD :: AC : AE.) **And if the Sides, or the Sides produced, be cut proportionally, the** Une DE, which joins the Points of Se8ion, ßall be parallel to the remaining Side of the Iriangle,... | |
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...demonstration will be the same. PROP. II. THEOR. IF a straight line be drawn parallel to one of the See N. **sides of a triangle, it shall cut the other sides,...be parallel to the remaining side of the triangle.** Let DE be drawn parallel to BC, one of the sides of the trian- • gle ABC : BD is to DA, as CE to... | |
| John Playfair - Trigonometry - 1806 - 311 pages
...same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. **IF a straight line be drawn parallel to one of the sides of a triangle, it** will cut the other sides, or the other sides produced proportionally ; and if the sides, or the sides... | |
| John Bonnycastle - Trigonometry - 1806 - 419 pages
...semicircle, or that which stands upon half the circumference, is a right angle, or 90°. 8. If a right **line be drawn parallel to one of the sides of a triangle, it** will cut the other sides proportionally. It may also be remarked, that some of the simplest cases of... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...Triangles and parallelograms of the same altitude are one to another as their, basesProp. II. Theor. **If a straight line be drawn parallel to one of the sides of a triangle, it shall** cat the other sides, or those produced, proportionally: and if the sides, or the sides produced, be... | |
| Euclides - 1814
...be drawn parallel to one of the See N. sides of a triangle, it shall cut the other sides, or these **produced,, proportionally : And if the sides, or the...be parallel to the remaining side of the triangle.** Join BE, CD ; then the triangle BDE is equal to the triangle CDE a , because they are on the same base... | |
| Euclides - Geometry - 1816 - 528 pages
...be drawn parallel to one of the See.N. sides of a triangle, it shall cut the other sides, or these **produced, proportionally : And if the sides, or the...be parallel to the remaining side of the triangle.** Let DE be drawn parallel to BC, one of the sides of the triangle ABC : BD is to DA, as CE to EA. -... | |
| John Playfair - Trigonometry - 1819 - 333 pages
...same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. **If a straight line be drawn parallel to one of the sides of a triangle, it** ' will cut the other sides, or the other sides produced, proportionally : And if the sides, or the... | |
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