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 7
... proportional between them . The roots of quantities are some- times expressed by means of fractional indices : thus , the cube root of AXBXC may be expressed by VAXBX C , or ( A × B × C ) , and so on . 28. Numbers in a parenthesis ...
... proportional between them . The roots of quantities are some- times expressed by means of fractional indices : thus , the cube root of AXBXC may be expressed by VAXBX C , or ( A × B × C ) , and so on . 28. Numbers in a parenthesis ...
Página 8
... proportional : thus , if ; then , A is to B as C to D. And the abbreviations of the proportion is , A : B :: C : D ; it is sometimes written A : B⇒C : D. DEFINITIONS . 1. " A POINT is that which has position , but not magnitude ...
... proportional : thus , if ; then , A is to B as C to D. And the abbreviations of the proportion is , A : B :: C : D ; it is sometimes written A : B⇒C : D. DEFINITIONS . 1. " A POINT is that which has position , but not magnitude ...
Página 107
... proportional between the other two . 10. When there is any number of magnitudes of the same kind , the first is said to have to the last the ratio compounded of the ratio which the first has to the second , and of the ratio which the ...
... proportional between the other two . 10. When there is any number of magnitudes of the same kind , the first is said to have to the last the ratio compounded of the ratio which the first has to the second , and of the ratio which the ...
Página 121
... proportional to two sides of another , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to the re- maining side of the first . 3. A straight line is said to be cut in ...
... proportional to two sides of another , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to the re- maining side of the first . 3. A straight line is said to be cut in ...
Página 123
... proportionally : And if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of section will be parallel to the remaining side of the tri- angle . Let DE be drawn parallel to BC , one of ...
... proportionally : And if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of section will be parallel to the remaining side of the tri- angle . Let DE be drawn parallel to BC , one of ...
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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...