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 Seiten |
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Seite 66
... radius of a circle is the straight line drawn from the centre to the circumference . I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one ...
... radius of a circle is the straight line drawn from the centre to the circumference . I. A straight line is said to touch a circle , when it meets the circle , and being produced does not cut it . II . Circles are said to touch one ...
Seite 102
... radius of the given circle , so that the rectangle contain- " ed by the whole and one of the parts may be equal to the square " of the other ( 11. 2. ) . Apply in the circle , on each side of a given " point , a line equal to the ...
... radius of the given circle , so that the rectangle contain- " ed by the whole and one of the parts may be equal to the square " of the other ( 11. 2. ) . Apply in the circle , on each side of a given " point , a line equal to the ...
Seite 106
... radius of the circle . And if through the points A , B , C , D , E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has ...
... radius of the circle . And if through the points A , B , C , D , E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has ...
Seite 158
... radius AC , the greater of the two sides , describe the circle CFG : produce AB to meet the circumfer- ence in E and F , and CB to meet it in G. Then because AF - AC , BF - AB + AC , the sum of the sides ; and since AE = AC , BE = AC ...
... radius AC , the greater of the two sides , describe the circle CFG : produce AB to meet the circumfer- ence in E and F , and CB to meet it in G. Then because AF - AC , BF - AB + AC , the sum of the sides ; and since AE = AC , BE = AC ...
Seite 165
... radius of the circle ; therefore also , because magnitudes have the same ratio with their equimultiples ( 15.5 . ) , the perimeter of the inscribed polygon is to the perimeter of the circumscribed , as the perpendicular from the centre ...
... radius of the circle ; therefore also , because magnitudes have the same ratio with their equimultiples ( 15.5 . ) , the perimeter of the inscribed polygon is to the perimeter of the circumscribed , as the perpendicular from the centre ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 36 - If two triangles have two sides of the one equal to two sides of the...
Seite 33 - ANY two sides of a triangle are together greater than the third side.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.