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" If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Pągina 147
per John Playfair - 1856 - 318 pągines
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 pągines
...QED PROP. C. THEOR. If 'from any angle of a triangle a straight line be drawn See N. perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pągines
...BGC to the sector EHF. Wherefore, in equal circles, &c. QED PROPOSITION B. See N. THEOn. — If an angle of a triangle be bisected by a straight line...rectangle contained by the segments of the base, together irith the square of the straight line tvhicli bisects the angle. Let ABC be a triangle, and let the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pągines
...QED PROP. C. THEOR. &* N. If from any angle of a triangle a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular, and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Mathematical Problems and Examples, Arranged According to Subjects, from the ...

1836 - 366 pągines
...cannot touch another in more points than one, whether it touches it on the inside or outside. 21. If an angle of a triangle be bisected by a straight line...the square of the straight line bisecting the angle. 22. The perimeters of similar rectilinear figures are in the simple ratio, and the areas in the duplicate...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 488 pągines
...line bisecting the angle. C. If from any angle of a triangle a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular, and the diameter of the circle described about the triangle. D. The rectangle contained...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 pągines
...if an exterior angle, &c. PROP. D. THEOR. IF from an angle of a triangle a perpendicular be drawn to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 290 pągines
...AD. PROPOSITION C. THEOREM. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Describe (IV. 5) the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 pągines
...as the arc BC, is to the arc EF, so is the sector BGC to the sector EHF. 149 . PROP. B. THEOR. If an angle of a triangle be bisected by a straight line, which likewise cuts the Lose; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pągines
...fi. ED PROP. C. THEOR. If from any angle of a triangle a straight line be drawn ' perpendicular to the base ; the rectangle contained by the sides of...the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. Let ABC be a triangle,...
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Geometrical Propositions Demonstrated, Or, a Supplement to Euclid: Being a ...

William Desborough Cooley - 1840 - 106 pągines
...; consequently, AD'AF = AF2+BF'FC, and since BA'AC =AD'AF, it follows, that BA'AC = AP + BF'FC, or the rectangle contained by the sides of the triangle, is equal to the square of the line bisecting the contained angle, together with the rectangle under the segments of...
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