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" If there be 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. Let... "
Elements of Plane Geometry - Page 63
by Thomas Hunter - 1878 - 132 pages
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...countries by square 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...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 parts...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...are at the opposite H B B K C ' angles of the parallelograms which make the gnomon.' PROP. I. THEOR. If there be two straight lines, one of which is divided...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...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...the 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...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...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...one " another. These signs will be occasionally used for brevity, " in what follows." PROP. I. THEOR. IF there be two straight lines, one of which is divided...rectangle contained by the two lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...have them ready to apply to the demonstration of the subsequent Propositions. PROPOSITION I. Theorem. If there be two straight lines, one of which is divided...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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...which are at the opposite angles of the parallelograms which make the gnomon. PROPOSITION I. THEOREM. If there be two straight lines, one of which is divided...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...'at the opposite angles of the paral- H 'lelograms which make the gnomon.' F D K BGC PROP. I. THEOR. IF there be two straight lines, one of which is divided...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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...at the opposite angles ' of the parallelograms, which make the gnomon.' 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...H " gnomon may also, for the sake of " brevity, be called the gnomon AGK "orEHC." B PROP. I. THEOR. If there be two straight lines, one of which is divided...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...
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