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, 1837 - 318 páginas |
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Página 61
... touch a circle , when it meets the cir- cle , and being produced does not cut it . And that line which has but one point in common with the circumference , is called a tangent , and the point in com- mon , the point of contact . 2 ...
... touch a circle , when it meets the cir- cle , and being produced does not cut it . And that line which has but one point in common with the circumference , is called a tangent , and the point in com- mon , the point of contact . 2 ...
Página 65
... 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 68
... 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 point A , and let F be the centre of ...
... 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 point A , and let F be the centre of ...
Página 69
... touch each other externally , the straight line which joins their centres will pass through the point of contact . A ; Let the two circles ABC , ADE , touch each other externally in the point and let F be the centre of the circle ABC ...
... touch each other externally , the straight line which joins their centres will pass through the point of contact . A ; Let the two circles ABC , ADE , touch each other externally in the point and let F be the centre of the circle ABC ...
Página 70
... touch another in the inside in more points than one . 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 AC ...
... touch another in the inside in more points than one . 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 AC ...
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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 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 12 - AB; but things which are equal to the same are equal to one another...
Página 80 - 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.
Página 288 - 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 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 81 - 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 this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.
Página 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Página 127 - 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.
Página 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Página 19 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.