 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...way, CL=CM. Now (Eucl. ii. 12.) .-. FD* and = 2 BC1 + BA' + AC\ + zBC x BM+ [2 BCx CM 2 BC1 = (46.) If a line be drawn parallel to the base of a triangle, and terminated in the sides ; to draw a line cutting it, and terminated also by the sides, so that... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...the squares of the lines joining them will be equal to five times the square of the hypothenuse. 46'. If a line be drawn parallel to the base of a triangle, and terminated in the sides; to draw a line cutting it, and terminated also by the sides, so that the... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...hence the squares of the sides are together equal to the squares of the diagonals. E THEOREM. 106. If a line be drawn parallel to the base of a triangle, it will divide the other sides proportionally. Let ABC be a triangle, and DE a straight line drawn... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...the squares of the sides are together equivalent to the squares of the diagonals. E C PROPOSITION XV. THEOREM. If a line be drawn parallel to the base of a triangle, it will divide, the. other sides proportionally. Let ABC be a triangle, and DE a straight line drawn... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...harmonically. be drawn bisecting the opposite sides, they will divide each other in the ratio of two to one. 4. If a line be drawn parallel to the base of a triangle...will bisect the base, and will be cut harmonically. 5. The inclination of two chords of a circle is measured by half the sum or half the difference of... | |
 | Charles Davies - Geometrical drawing - 1840 - 264 pages
...AC. This is called the carpenter's theorem. PART I. — SECTION VI. Properties of the Triangle. 11. If a line be drawn parallel to the base of a triangle, it will cut the two other sides proportionally. Thus, if DE be drawn parallel to the base BC, we shall... | |
 | Nathan Scholfield - 1845 - 894 pages
..... . (a+W . (a— b)3 , . ,, cal formula, v— £ |-v— „— =a5-f-6. ** ' <fc PROPOSITION XIV. THEOREM. If a line be drawn parallel to the base of a triangle, it will divide t/te sides proportionally. Let ABC be a triangle, and DE a straight line drawn parallel... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...correspond 1.. 0 ...embers together,and observing that BE and DE are equal, we shall have PROPOSITION XV. THEOREM. If a line be drawn parallel to the base of a triangle, it will diviu the other sides proportionally. Let ABC be a triangle, and DE a straight line drawn parallel... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...is equal to the number in the two small squares. Of Triangle Sides cut Proportionally. THEOREM XIII, If a line be drawn parallel to the base of a triangle^ it will divide the other two sides proportionally. Let ABC be any triangle, and DE a straight line... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...the number in the two small squares. 94 Of Triangle Sides cut Pr opor t ion a 1 1 y . THEOBEM XIII. If a line be drawn parallel to the base of a triangle, it will divide the other two sides proportionally. Let ABC be any triangle, and DE a straight line... | |
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ABC be a triangle, and DE a straight line drawn parallel to the base BC ; then will AD : DB : : AE : EC. 
