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 TrignonometryBell & Bradfute, 1875 - 257 pagine |
Dall'interno del libro
Risultati 1-5 di 52
Pagina 2
... perpendicular to it . VIII . An obtuse angle is that which is greater than a right angle . IX . An acute angle is that which is less than a right angle . X. A figure is that which is enclosed by one or more boundaries . The space ...
... perpendicular to it . VIII . An obtuse angle is that which is greater than a right angle . IX . An acute angle is that which is less than a right angle . X. A figure is that which is enclosed by one or more boundaries . The space ...
Pagina 10
... perpendicular to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
... perpendicular to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
Pagina 39
... perpendicular falls , and the straight line intercepted be- tween the perpendicular and the obtuse angle . * Let ABC be an obtuse - angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ( I. 12 ) perpendicular ...
... perpendicular falls , and the straight line intercepted be- tween the perpendicular and the obtuse angle . * Let ABC be an obtuse - angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ( I. 12 ) perpendicular ...
Pagina 40
... perpendicular to BC ; then is BC the straight line between the perpen- B C dicular and the acute angle at B ; and it is manifest that ( I. 47 ) AB2 + BC2 = AC2 + 2BC2 = AC + 2BC.BC . Therefore , in every tri- angle , & c . Q. E. D. PROP ...
... perpendicular to BC ; then is BC the straight line between the perpen- B C dicular and the acute angle at B ; and it is manifest that ( I. 47 ) AB2 + BC2 = AC2 + 2BC2 = AC + 2BC.BC . Therefore , in every tri- angle , & c . Q. E. D. PROP ...
Pagina 41
... perpendicular to BC ; and because BEA is a right angle , AB2 = ( I . 47 ) BE2 + AE2 and AC2 = CE2 + AE2 ; wherefore AB2 + AC2BE2 + CE2 + 2AE2 . But be- cause the line BC is cut equally in D , B D E and unequally in E , BE2 + CE2- ( II ...
... perpendicular to BC ; and because BEA is a right angle , AB2 = ( I . 47 ) BE2 + AE2 and AC2 = CE2 + AE2 ; wherefore AB2 + AC2BE2 + CE2 + 2AE2 . But be- cause the line BC is cut equally in D , B D E and unequally in E , BE2 + CE2- ( II ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore given circle given point given straight line hypotenuse inscribed less Let ABC Let the straight meet multiple opposite angle parallel parallelogram perpendicular plane polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles segment semicircle similar sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC straight line drawn tangent THEOR third three straight lines touches the circle triangle ABC triangle DEF wherefore