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 TrigonometryPrinted and published at no. 24 Arch Street, A. Walker, Agent, 1832 - 333 páginas |
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Página 66
... touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one another , which meet , but do not cut one another . III . Straight lines are said to be equally dis- tant from the ...
... touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one another , which meet , but do not cut one another . III . Straight lines are said to be equally dis- tant from the ...
Página 70
... touch one another internally , they cannot have the same centre . Let the two circles ABC , CDE , touch one another internally in the point C : they have not the same centre . For , if they have , let it be F ; join FC , and draw any ...
... touch one another internally , they cannot have the same centre . Let the two circles ABC , CDE , touch one another internally in the point C : they have not the same centre . For , if they have , let it be F ; join FC , and draw any ...
Página 73
... touch each other internally , the straight line which joins their centres being produced , will pass through the point of contact . Let the two circles ABC , ADE , touch each other internally in the K point A , and let F be the centre ...
... touch each other internally , the straight line which joins their centres being produced , will pass through the point of contact . Let the two circles ABC , ADE , touch each other internally in the K point A , and let F be the centre ...
Página 74
... touch each other externally , the straight line which joins their centres will pass through the point of contact . Let ... touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more ...
... touch each other externally , the straight line which joins their centres will pass through the point of contact . Let ... touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more ...
Página 75
... touch another in the inside in more points than one . A C K Nor can two circles touch one another on the outside in more than one point : For , if it be possible , let the circle ACK touch the circle ABC in the points A , C , and join ...
... touch another in the inside in more points than one . A C K Nor can two circles touch one another on the outside in more than one point : For , if it be possible , let the circle ACK touch the circle ABC in the points A , C , and join ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY square straight line AC THEOR third touches the circle triangle ABC wherefore
Pasajes populares
Página 56 - 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 41 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Página 36 - If two triangles have two sides of the one equal to two sides of the...
Página 33 - ANY two sides of a triangle are together greater than the third side.
Página 19 - 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.
Página 308 - 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 25 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Página 56 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 90 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.