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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.
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Page 32
by Daniel Cresswell - 1817 - 436 pages

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...the gnomon ' AGK, or EHC.' PROP. I. THEOR. IF there be two straight lines, one of which is divided into any number of parts, the rectangle contained...lines is equal to the rectangles contained by the undivided line and the several parts of the divided line. Let A and BC be two straight lines, and let...

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...rallelograms which make the gnomon.' G PROP. I. THEOR. IF there be two straight lines, one of which is divided into any number of parts ; the rectangle contained...lines, is equal to the rectangles contained by the undivided line and the several parts of the divided line. D K H Book II. Let A and BC be two straight...

## Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...complements, is called a gnomon. Prop. I. Theor. If there be two straight lines, one of which is divided into any number of parts; the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Prop. II. Theor. If a straight line be divided...

## An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...parts a, b, and c, of the divided line s." QED Cor. Hence, if two given straight lines be each divided into any number of parts, the rectangle contained by the two straight lines will be equal to the sum of the rectangles contained by each of the parts of the one, and each of the...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...' which makes the gnomon.' PROP. I. THEOR. IF there be two straight lines, one of which is divided into any number of parts; the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. BouK II. Let A and BC be two straight lines...

## A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...the other two sides as diameters. SUPPLEMENT TO THE ELEMENTS OF EUCLID. BOOK II. PROP. I. 1. THEOREM. If two given straight lines be divided, each into...parts of the one and the several parts of the other. Let the given straight line AB be divided into EFB >*. I II N K LM CGD t any parts in the points E,...

## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...gnomon AGK or ' EHC." DEC PROP. I. THEOR. . . If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained...lines is equal to the rectangles' contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...

## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...make the gnomon.' Propońlion. 7. Theorem» If there be two straight lines, one of which is divided into any number of parts ; the rectangle contained...lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines ; and...