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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 Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...various other places, but particularly in this book. E С К. i H PROPOSITION I. THEOBEM. If there be two straight lines, one of which is divided into any...contained by the two straight lines, is equal to the rectangle contained by the undivided line, and the several parts of the divided line. Let A and B С...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...but CAD is a right angle, wherefore CAB is also a right angle. XLVIII.— EUCLID II. 1. If there be two straight lines one of which is divided into any...the several parts of the divided line. Let A and BC (Fig. 38) be two straight lines whereof BC is divided into parts by the points D, E, etc. The rectangle...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...the other two sides of it ; the angle contained by these two sides is a right angle. 6. If there be two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line. 7. To describe a square that shall be equal to a given rectilineal figure. 8. If two circles cut one...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...subtending the right angle is equal to the square under the sides containing the right angle. If there be two straight lines, one of which is divided into any...number of parts, the rectangle contained by the two lines is equal to the rectangles contained by the undivided line, and the several parts of the divided...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...The learner is supposed to be familiar with most of them. PROP. 1. — THEOREM. If there be two st. lines, one of which is divided into any number of parts, the rectangle contained by the two st. lines is equal to the rectangles contained by the undivided line and the several parts of the divided...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858
...is divided into tunj number of parts, the rectangle continued by the two st. lines is equal to tlie rectangles contained by the undivided line and the several parts of the divided line. Соя. V. 11. 3, 31, I. OEM. :UI, AT. Я. K. 1 Hjp. Concl. h...,ii n '., я. I MI ; .;. I. : :J1....
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...which are at the opposite angles of the parallelograms which make the gnomon. _D—..E_ C H there be two straight lines, one of which is divided into any...undivided line, and the several parts of the divided line. Given the two straight lines A and BC, and let BC be divided into any parts in the points D, E ; to...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...sometimes " the rectangle ABC." To this proposition may be added the corollary : If two straight lines be divided into any number of parts, the rectangle contained...lines, is equal to the rectangles contained by the several parts of one line and the several parts of the other respectively. The method of reasoning...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...( AB+ CD) x EF. Hence the theorem ; the area of a trapezoid, etc. THEOREM XXXV. If one of two lines is divided into any number of parts, the rectangle contained by the two lines is equal to the sum of the several rectangles contained by the undivided line and tJ.c several...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...of which is dicided into any number of parts, the rectangle contained by the tiro straight lin<!,< is equal to the rectangles contained by the undivided line, and the several parts of the divided line. , (References— Prop. I. 3, 11, 31, 34.) Hypothesis. — Let A and BC be two straight lines ; and...
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