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 39
Pagina 43
... . VIII . The sector of a circle is the figure con- tained by two straight lines drawn from the centre , and the arc of the circumference between them . IX . Similar segments of a circle are those in BOOK THIRD . 43 'BOOK THIRD. ...
... . VIII . The sector of a circle is the figure con- tained by two straight lines drawn from the centre , and the arc of the circumference between them . IX . Similar segments of a circle are those in BOOK THIRD . 43 'BOOK THIRD. ...
Pagina 44
... Similar segments of a circle are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw within ...
... Similar segments of a circle are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw within ...
Pagina 56
... similar to the segment ADB , and similar segments of circles contain ( III . Def . 9 ) equal angles , the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( I. 16 ) . Therefore , there cannot be ...
... similar to the segment ADB , and similar segments of circles contain ( III . Def . 9 ) equal angles , the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( I. 16 ) . Therefore , there cannot be ...
Pagina 57
... similar segments of circles upon the same side of the same line which do not coincide . Q. E. D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one another . Let AEB , CFD be similar segments of ...
... similar segments of circles upon the same side of the same line which do not coincide . Q. E. D. PROP . XXIV . THEOR . Similar segments of circles upon equal straight lines are equal to one another . Let AEB , CFD be similar segments of ...
Pagina 58
... similar ( III . Def . 9 ) to the segment EDF ; and they are upon equal straight lines K H CE F L BC , EF : but similar segments of circles upon equal straight lines are equal ( III . 24 ) to one another ; therefore the segment BAC is ...
... similar ( III . Def . 9 ) to the segment EDF ; and they are upon equal straight lines K H CE F L BC , EF : but similar segments of circles upon equal straight lines are equal ( III . 24 ) to one another ; therefore the segment BAC is ...
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Elements of Geometry; Containing the First Six Books of Euclid, With Two ... John 1748-1819 Playfair Anteprima non disponibile - 2021 |
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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