| Robert Potts - 1868 - 410 pages
...the rectangle contained by their sum AD and their difference DB. PROPOSITION VI. THEOREM. Tfaitraight **line be bisected, and produced to any point; the rectangle contained by the whole line thus** prodlwed, and the part of it produced, together with the square on half the line bisected, i3 equal... | |
| frank smith - 1868
...angles of a triangle can in no case exceed two right angles. 4. Give two proofs of Eucl. I. 47. 5. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Woolwich roy. military acad - 1868
...the magnitudes of the angles of the different triangles referred to, complete the demonstration : " **If a straight line be bisected and produced to any point, the** squares of the whole line thus produced and the part of it produced are together double of the square... | |
| Civil service - 1869 - 178 pages
...shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 3. **If a straight line be bisected, and produced to any...square of half the line bisected, is equal to the** straight line which is made up of the half and the part produced. 4. The diameter is the greatest straight... | |
| Henry Green - 1870
...4 = 12 + 4 = 16 : extracting the square root, x + 2 = 4 /. x = 2. PROP. 6. — THEOR. If a st. tine **be bisected and produced to any point, the rectangle...half the line bisected, is equal to the square of the** st. line which is made up of the half and the part produced. CONS.— 46. I., Pst. 1, and 31. I. DEM.—... | |
| Euclides - 1871
...in D, shew that the sum of the squares on AB, AC is equal to twice the sum of the squares on AD, BD. **If a straight line be bisected and produced to any point, the** square on the whole line thus produced and the square on the part of it produced are together double... | |
| BENJAMIN HALLOWELL - 1872
...side to which it is parallel in the triangle ABC, and each rhombus is half of ABC. THEOREM II. — **If a straight line be bisected and produced to any point, the rectangle** of the whole line thus produced and the part produced, with the square of half the line bisected, are... | |
| Euclides - 1872
...parallelograms is equal to twice the triangle BKD. II. 11. Produce a given straight line to a point such that **the rectangle contained by the whole line thus produced and the part** produced shall bo equal to the square on the given straight line. in. 22. If the opposite sides of... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...of the squares on AB, AC is equal to twice the sum of the squares on AD, BD. PROPOSITION X. THEOREM. **If a straight line be bisected and produced to any point, the** square on the whole line thus produced and the square on the part of it produced are together double... | |
| Euclid, C. P. Mason - Geometry - 1872
...the Qs on AD and DB is equal to twice the Q on AC together with twice the Q on C D. PBOPOSITION X. **If a straight line be bisected and produced to any point, the** square on the whole line thus formed together with the square on the produced part, is equal to twice... | |
| |