 | Euclides - 1846 - 292 pages
...of any figure is the straight line drawn from its vertex perpendicular to the base. PROP. I. THEOR. Triangles and parallelograms of the same altitude are to one another as their bases. Let the triangles ABC, ACD, and the parallelograms EC, CF, have the same altitude, viz. the perpendicular... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...solid AB to the solid CD. COR. 1. From this it is manifest; that prisms upon triangular bases, and of the same altitude, are to one another as their bases. Let the prisms BNM, DPG, the bases of which are the triangles AEM, CFG, have the same altitude : complete... | |
 | Great Britain. Council on Education - Education - 1848 - 532 pages
...circle in a given square. 0. Ratios that are equal to the same ratio are equal to one another. • 6. Triangles and parallelograms of the same altitude are to one another as their bases. 7. In equal circles, angles, whether at the centres or circumferences, have the same ratio which the... | |
 | Great Britain. Committee on Education - 1848 - 606 pages
...deduce the equation to the circle referred to rectangular co-ordinates. Section 4. 1. The areas of triangles and parallelograms of the same altitude are to one another as their bases. 2. Shew that the areas of similar triangles are to one another in the duplicate ratio (or as the squares)... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...deduce the equation to the circle referred to rectangular co-ordinates. SECTION IV. 1. The areas of triangles and parallelograms of the same altitude are to one another as their bases. A portion of a triangle, next to one angle, is cut off by a line parallel to the opposite side, and... | |
 | Great Britain. Committee on Education - Education - 1848 - 514 pages
...than a semicircle is greater than a right angle. 4. To describe a circle in a given square. cxxxvu 6. Triangles and parallelograms of the same altitude are to one another as Iheir bases. 7. In equal circles, angles, whether at the centres or circumferences, have the same ratio... | |
 | Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...it and its greater segment is similarly divided. 2. To describe a circle about a given triangle. 3. Triangles and parallelograms of the same altitude are to one another as their bases. Section 4. 1. Enunciate and prove Pror>. XLVII., Book I. 2. In equal circles equal arches are subtended... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...to the base В С, is the altitude of the triangle А В С, at page 149. PROPOSITION I.— THEOREM. Triangles and parallelograms of the same altitude are to one another as their bases. Let the triangles ABC, ADK, and the parallelograms E С, FD, have the same altitude : then as the base... | |
 | Euclides - 1855 - 270 pages
...perpendicular drawn from any angular point to the base, or base produced, is the altitude. PROP. I. THEOREM. Triangles and parallelograms of the same altitude are to one another as their bases. Let the triangles ABС and A С D, and the parallelograms E С and OF, have the same altitude, viz., the... | |
 | Euclides - 1855 - 230 pages
...the solid AB to the solid CD. COROLLARY. From this it is manifest, that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the prisms, the bases of which are the triangles AEM, CFG, and NBO, PDQ the triangles opposite to them,... | |
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Triangles and parallelograms of the same altitude are to one another as their bases. 
