Books Books If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... Elements of geometry, containing the first two (third and fourth) books of ... - Page 86
by Euclides - 1871 ## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid... ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...the rectangle contained by the lines together with the square of the difference of the lines. VIII. If a straight line be divided into any two parts,...line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and the... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...contained by the " lines together with the square of the difference of the " lines." PROP. VIII. THEOR. If a straight line be divided into any two parts,...contained by the whole line, and one of the parts, togetiier with the square of the other part, is equal to the square of the straight line which is made... ## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...KF, and that these = 2 AH + KF ; ;and that these = 2 AB x BC + AC*. CBD PROPOSITION VIII. Theorem. If a straight line be divided into any two parts,...line and one of the parts, together with the square of the other part, is equal to the square of the line made up of the whole and that part. R In the... ## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...are equal to twice the rectangle AB-BC, together with the square of AC. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts,...line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and the... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...equal to the square of their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be divided into any two parts, four times the rectangle contained by the whole and one of the parts, together with the square of the other part, is equal to the square of the straight... ## Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 254 pages
...a c. M.—Express this truth in words. P.—If a straight line be divided into any two parts, twice the rectangle contained by the whole line and one of the parts is equal to twice the square upon that part, together with twice the rectangle contained by the parts.... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...rectangle AB, BC, together with the square AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Ir a straight line be divided into any two parts, four...line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... ## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...AC. Wherefore, if a straight line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided into any two parts, four times the rectangle contained...line and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made up of the whole and that... 