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 páginas |
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Página 11
... doubles of the same thing , are equal to one another . which are halves of the same thing , are equal to one another . 8. Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... doubles of the same thing , are equal to one another . which are halves of the same thing , are equal to one another . 8. Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Página 34
... double ( 34. 1. ) of the triangle BDC ; and they are therefore equal to one an- other . B F But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ...
... double ( 34. 1. ) of the triangle BDC ; and they are therefore equal to one an- other . B F But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ...
Página 36
... double of the triangle . Let the parallelogram ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is ...
... double of the triangle . Let the parallelogram ABCD and the tri- angle EBC be upon the same base BC and between the same parallels BC , AE ; the parallelogram ABCD is double of the trian- gle EBC . Join AC ; then the triangle ABC is ...
Página 37
... double of the triangle AEC . And the paral- lelogram FECG is likewise double ( 41. 1. ) of the triangle AEC , because it is upon the same base , and between NI D B E C the same parallels : Therefore the parallelogram FECG is equal to ...
... double of the triangle AEC . And the paral- lelogram FECG is likewise double ( 41. 1. ) of the triangle AEC , because it is upon the same base , and between NI D B E C the same parallels : Therefore the parallelogram FECG is equal to ...
Página 40
... double ( 41. 1. ) of the triangle ABD , because they are upon the same base , BD , and between the same parallels , BD , AL ; and the square GB 1 is double of the triangle BFC be- cause these also 40 ELEMENTS.
... double ( 41. 1. ) of the triangle ABD , because they are upon the same base , BD , and between the same parallels , BD , AL ; and the square GB 1 is double of the triangle BFC be- cause these also 40 ELEMENTS.
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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 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
Pasajes populares
Página 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.
Página 74 - THE angles in the same segment of a circle are equal to one another...
Página 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.
Página 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.
Página 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 '
Página 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.
Página 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.
Página 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.
Página 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.
Página 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.