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" PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 50
by Euclides - 1841 - 351 pages
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The Geometrical Companion: In which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 169 pages
...upon right lines, one foot, one yard, &c. &c. in length respectively. ART. 89. " If there be two right lines, one. of which is divided into any number of parts, the rectangle under the two lines is equal to the sum of the rectangles under the undivided line and the several...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...2y = s — d, ,-.y — (s — d), which is the second part. PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided into any number of pans, the rectangle contained by the two lines is equal to the sum of the rectangles cont.tined by...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...divided into any number of partt, the rectangle contained by the tiro lines shall be equal to tht sum of the rectangles contained by the undivided line, and the several parts of the tliridfd line. Let AB and С be two straight lines, of which AB is divided into the parts AI), DE,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...the sake of brevity, be Jj fj. Q " called the gnomon AGK or "EEC." AE DEC PROP. I. THEOR. If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained by tlte two straight lines is equal to the rectangles contained by the undivided line, and the several...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833
...EGF. END OF FIRST BOOK. THE SECOND BOOK, IN GENERAL TERMS. PROPOSITION 1. THEOR. If there be two right lines, one of which is divided into any number of parts, the rectangle under the two linns is equal to the sum of the rectangles under the undivided line and the several...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...for the ' sake of brevity, be called the gno' mon AGK or EHC." A. E H I PROP. I. THEOR. If there be two straight lines, one of which is divided into any...the rectangle contained by the two straight lines is equ2l to the rectangles contained by the undivided line, and the several parts of the divided line....
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...miles. SECTION 5. Rectangles under the par Is of divided lines. PROP. 30. (Eue. ii. 1.) If there be two straight lines, one of which is divided into any...number of parts, the rectangle contained by the two lines shall be equal to the sum of the rectangles contained by the undivided line, and the several...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...parallelograms about a diameter, together with the two complements, is called a Gnomon. PHOP. I. If there be two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line. II. If a straight line be divided into any two parts, the rectangles contained by the whole and each...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 128 pages
...extremities of equal arches, and not intersecting, are parallel, 64. ART. 89. If there he two right lines, one of which is divided into any number of parts, the rectangle under the two lines is equal to the sum of the rectangles under the undivided line and the several...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...ready to apply to the demonstration of the subsequent Propositions. PROPOSITION I. Theorem. If there be two straight lines, one of which is divided into any...contained by the two straight lines is equal to the & rectangles contained by the undivided line, and the several parts of the divided line. JL LH CB Proved...
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