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, 1846 - 317 sider |
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Side 11
... doubles of the same thing , are equal to one another . 7. Things 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 ...
... doubles of the same thing , are equal to one another . 7. Things 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 ...
Side 34
... double ( 34. 1. ) of the triangle BDC ; and they are therefore equal to one an- other . B D F C But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then ...
... double ( 34. 1. ) of the triangle BDC ; and they are therefore equal to one an- other . B D F C But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then ...
Side 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 ...
Side 37
... double of the triangle AEC . And the paral- lelogram FECG is likewise double ( 41. 1. ) of the triangle AEC , because upon the same base , and between it is N B E D the same parallels : Therefore the parallelogram FECG is equal to the ...
... double of the triangle AEC . And the paral- lelogram FECG is likewise double ( 41. 1. ) of the triangle AEC , because upon the same base , and between it is N B E D the same parallels : Therefore the parallelogram FECG is equal to the ...
Side 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 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 is double of the triangle BFC be- cause these also 40 ELEMENTS.
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Vanlige uttrykk og setninger
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 magnitudes meet multiple 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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 49 - 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.
Side 147 - ... cuts 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.
Side 292 - 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.
Side 7 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 139 - K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes.
Side 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...
Side 125 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 131 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Side 78 - 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.