Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ...J. Eastburn & Company, 1819 - 317 σελίδες |
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Αποτελέσματα 6 - 10 από τα 85.
Σελίδα 40
... parallel to CD ( 27. 1. ) ; but AB is also parallel to CD ; therefore two straight lines are drawn through the same point G , parallel to CD , and yet not coinciding with one an- other , which is impossible C ( 11. Ax . ) . The angles ...
... parallel to CD ( 27. 1. ) ; but AB is also parallel to CD ; therefore two straight lines are drawn through the same point G , parallel to CD , and yet not coinciding with one an- other , which is impossible C ( 11. Ax . ) . The angles ...
Σελίδα 41
... parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. PROP . XXXI . E PROB . To draw a straight line through a given point parallel to a given straight line . A D Let A be the given point , and BC the given straight ...
... parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. PROP . XXXI . E PROB . To draw a straight line through a given point parallel to a given straight line . A D Let A be the given point , and BC the given straight ...
Σελίδα 42
... parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two ...
... parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two ...
Σελίδα 43
... parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and parallel . Join BC ; and because AB is pa- rallel to CD , and BC meets them ...
... parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and parallel . Join BC ; and because AB is pa- rallel to CD , and BC meets them ...
Σελίδα 44
... parallels , are equal to one another . M ( SEE THE 2d and 3d figures . ) Let the parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF ...
... parallels , are equal to one another . M ( SEE THE 2d and 3d figures . ) Let the parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference common section cosine cylinder demonstrated diameter draw drawn 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 parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...
Σελίδα 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.
Σελίδα 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 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.
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 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.
Σελίδα 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Σελίδα 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.