Elements of Geometry: Containing the First Six Books of Euclid with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryJ.P. Lippincott & Company, 1855 - 318 páginas |
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Página 8
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , * The definitions marked with inverted commas are different from those of Euclid ...
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , * The definitions marked with inverted commas are different from those of Euclid ...
Página 13
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the ...
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the ...
Página 14
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , so that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , so that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
Página 15
... triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two ...
... triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two ...
Página 16
... angle which is contain ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
... angle which is contain ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 41 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 70 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Página 91 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 273 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...