| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...be drawn from G to B and from G to D, show that BGD is a straight line. PROPOSITION VIII. THEOREM. **If a straight line be divided into any two parts,...one of the parts, together with the square on the** otJter part, is equal to the square on the straight line which is made up of the \ and the first part.... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, **the rectangle contained by the whole line and one of the parts** is equal to the square on that part together with the rectangle contained by the two parts. The propositions... | |
| Henry Major - Student teachers - 1873 - 588 pages
...squares of A] ! and BC are equal to twice the rectangle AB, BC. together with the square of AC. VIII. — **If a straight line be divided into any two parts four times the rectangle contained by the** wJwle line, and one of the parts, together with the square oftha other part, is equal to the square... | |
| Edward Atkins - 1874 - 428 pages
...together with the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. **If a straight line be divided into any two parts,...contained by the whole line and one of the parts,** toget/ier with the square on the other part, is equal to the square on tlie straight line which is... | |
| Euclides - 1874 - 120 pages
...line thus produced, and the part of it produced, together with the square on half the line bisected, **is equal to the square on the straight line which is made up of the** half and the part produced. j Let the straight line AB he hisected at the point ' • C, and produced... | |
| Braithwaite Arnett - 1874 - 130 pages
...line thus produced, and the part of it produced, together with the square on half the line bisected, **is equal to the square on the straight line which is made up of the** half and the part produced. 4. If a straight line drawn through the centre of a circle bisect a straight... | |
| Euclides - 1874 - 342 pages
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that **the rectangle contained by the whole line, and one of the parts,** shall be equal to the square on the other part. Construction. Upon AB describe the square ACDB (I.... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, **the rectangle contained by the whole line and one of the parts** is equal to the square on that part together with the rectangles contained by that part and the other... | |
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...BC. <^. E. D, PROP. III. — THEOREM. (Euc. II. 3.) If a straight line be divided into any two parts, **the rectangle contained by the whole line and one of the parts,** is equal to the square of that part, together with the rectangle contained by the two parts. Let AB... | |
| Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...be drawn from G to B and from (f to D, shew that BO D ia a straight line. PROPOSITION VIII. THEOREM. **If a straight line be divided into any two parts, four times the rectangle contained by** ike whole line and one of the parts, together with the square on the other part, is equal to the square... | |
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