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 49
... one of which is divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line ... whole and each of the parts , are together equal to the square of the whole ...
... one of which is divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line ... whole and each of the parts , are together equal to the square of the whole ...
Side 50
... line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . Let the straight line AB be divided ...
... line be divided into any two parts , the rectangle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . Let the straight line AB be divided ...
Side 52
... line be bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the ... parts , the squares of the whole line , and of one of the parts , are equal to twice the rectangle contained by the ...
... line be bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the ... parts , the squares of the whole line , and of one of the parts , are equal to twice the rectangle contained by the ...
Side 53
... the rectangle contained by the lines together with the square of " the difference of the lines . " SCHOLIUM . In ... line be divided into any two parts , four times the rectangle con- tained by the whole line , and one of the parts ...
... the rectangle contained by the lines together with the square of " the difference of the lines . " SCHOLIUM . In ... line be divided into any two parts , four times the rectangle con- tained by the whole line , and one of the parts ...
Side 54
... the rectangle AG is equal to MP , and PL to RF : but MP is equal ( 43. 1. ) to PL , because they are the complements of the parallelogram ML ; wherefore AG is equal also to RF . Therefore the four rectangles AG , MP , PL , RF , are equal to ...
... the rectangle AG is equal to MP , and PL to RF : but MP is equal ( 43. 1. ) to PL , because they are the complements of the parallelogram ML ; wherefore AG is equal also to RF . Therefore the four rectangles AG , MP , PL , RF , are equal to ...
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Almindelige termer og sætninger
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
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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.