| Euclides - 1847
...if a line be drawn from the vertex perpendicular to the base, the difference of the squares of the **sides is equal to the difference of the squares of the segments of the base.** PART. ENUN. — Let ABC be any A ; from the vertex A draw AD X to the base BC; then the difference... | |
| Euclid, Robert Potts - Euclid's Elements - 1847 - 478 pages
...true; then by Euc. vi. 16, it follows that the difference of the squares of the sides of the triangle, **is equal to the difference of the squares of the segments of the base** ; and therefore the difference of the squares of one side and the adjacent segment of the base, is... | |
| Euclides - 1849
...if a line be drawn from the vertex at right angles to the base, the difference of the squares of the **sides is equal to the difference of the squares of the segments of the base.** 6. If from one of the acute angles of a right-angled triangle, a line be drawn to the opposite side,... | |
| George Roberts Perkins - Geometry - 1850 - 320 pages
...Geometry, conducting as it does to the solution of so many important problems. PROPOSITION IX. THEOREM. **In any triangle, the difference of the squares of...of the two lines or distances included between the** extremities of the base and the perpendicular, drawn from the vertical angle to the base, or to the... | |
| H.N. ROBINSON - 1851
...be drawn from the vertical angle of any triangle to the base, the difference of the squares of the **sides is equal to the difference of the squares of the segments of the base.** Let ABC be any triangle. Take the longer side as a base, and from the opposite angle let fall the perpendicular... | |
| Euclides - 1852
...if a line be drawn from the vertex at right angles to the base; the difference of the squares of the **sides is equal to the difference of the squares of the segments of the base.** In any triangle, if a line be drawn from the vertex bisecting the base; the sum of the squares of the... | |
| Euclides - 1862
...to the difference of two given squares. 49. The difference of the squares of the sides of a triangle **is equal to the difference of the squares of the segments of the base** made by a perpendicular from the opposite angle. 50. The three straight lines bisecting the three angles... | |
| Horatio Nelson Robinson - Conic sections - 1865 - 444 pages
...be drawn from the vertical angle of any triangle to the base, the difference of the squares of the **sides is equal to the difference of the squares of the segments of the base.** 27. The square described on the side of an equilateral triangle, is equal to three times the square... | |
| John Playfair, Euclid - Geometry - 1855 - 317 pages
...isosceles; BC2=2AB2=2AC2 ; therefore, BC = ABv/2. COR. 3. Hence, also, if two right angled triangles have **two sides of the one, equal to two corresponding sides of the other ; their third** side* will also be equal, and the triangles will be identical. PROP. XLVIII. THEOR. If tfie square... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 283 pages
...said hypothenuse and other side (th. 33). Corol. 2. Hence, also, if two right-angled triangles have **two sides of the one equal to two corresponding sides...triangle, the difference of the squares of the two sides** w equal to the difference of the squares of the segments of the base, or of the two lines or distances... | |
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