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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. "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 72
by Euclides - 1860
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 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...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 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...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 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...
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Elementary Geometry: With Applications in Mensuration

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...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 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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