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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 sider |
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Resultat 1-5 av 30
Side 20
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles СВА , ВАС . Bisect ( 10. 1. ) AC in E , join BE and produce ...
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles СВА , ВАС . Bisect ( 10. 1. ) AC in E , join BE and produce ...
Side 21
... 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- A easy B C gether equal ( 13. 1. ) to two right an- D gles 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- A easy B C gether equal ( 13. 1. ) to two right an- D gles therefore the ...
Side 23
... interior and opposite angle , the exte- rior 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 exte- rior 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 ...
Side 27
... interior and opposite angle BCA , which is impossible ( 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 impossible ( 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 ...
Side 28
... interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH ...
... interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1839 |
Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1856 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition 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 line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane 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 AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 41 - 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.
Side 70 - 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.
Side 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Side 91 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 273 - 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...
Side 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...