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 1 - 5 από τα 30.
Σελίδα 31
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it ...
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it ...
Σελίδα 32
... interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- B A C Ꭰ gether equal ( 13. 1. ) to two right angles ; therefore the ...
... interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- B A C Ꭰ gether equal ( 13. 1. ) to two right angles ; therefore the ...
Σελίδα 34
... interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
... interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
Σελίδα 38
... interior and opposite angle BCA : which is im- possible ( 16. 1. ) wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two AB , BC , are equal to the two DE , EF , each to each ; and ...
... interior and opposite angle BCA : which is im- possible ( 16. 1. ) wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two AB , BC , are equal to the two DE , EF , each to each ; and ...
Σελίδα 39
... interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon ...
... interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon ...
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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.