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 TrigonometryW.E. Dean, 1853 - 317 σελίδες |
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Σελίδα 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 AXBXC , or ( AXBXC ) , and so on . 28. Numbers in a parenthesis , such as ...
... 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 AXBXC , or ( AXBXC ) , and so on . 28. Numbers in a parenthesis , such as ...
Σελίδα 8
... proportional : thus , if A C 1 be B D ; 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 ...
... proportional : thus , if A C 1 be B D ; 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder 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 Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 51 - 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.
Σελίδα 74 - THE angles in the same segment of a circle are equal to one another...
Σελίδα 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Σελίδα 29 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Σελίδα 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Σελίδα 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Σελίδα 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.