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 13
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
... bases , or third sides , shall be equal ; and the areas of the triangles shall be equal ; and their other angles shall be ... base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are ...
Página 14
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
Página 15
... base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
... base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a ... base DC is equal to the base AB , and the area of the triangle DBC is equal to that of the triangle ( 4. 1. ) ACB , the ...
Página 16
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Página 17
... base EF , and upon side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but ...
... base EF , and upon side of it , there can be two triangles EDF , EGF , that have their sides which are terminated in one extremity of the base equal to one another , and like- wise their sides terminated in the other extremity ; but ...
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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...