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 32
Pagina 65
... FOURTH . DEFINITIONS . I. A rectilineal figure is said to be inscribed in another rectili- neal figure , when all the angles of the in- scribed figure are upon the sides of the figure in which it is inscribed , each upon each . II . In ...
... FOURTH . DEFINITIONS . I. A rectilineal figure is said to be inscribed in another rectili- neal figure , when all the angles of the in- scribed figure are upon the sides of the figure in which it is inscribed , each upon each . II . In ...
Pagina 67
... demonstrated to be equal to DFE ; and therefore the remaining angle MLN is equal ( I. 32 ) to the remaining angle EDF ; wherefore the triangle LMN is equiangular to the triangle DEF ; and it is described BOOK FOURTH . 67.
... demonstrated to be equal to DFE ; and therefore the remaining angle MLN is equal ( I. 32 ) to the remaining angle EDF ; wherefore the triangle LMN is equiangular to the triangle DEF ; and it is described BOOK FOURTH . 67.
Pagina 69
... , BD of the circle ABCD , at right angles to one another , and through the points A , B , C , D draw ( III . 17 ) FG , GH , HK , KF touching the circle ; and because B F E D FG touches the circle ABCD , BOOK FOURTH . 69.
... , BD of the circle ABCD , at right angles to one another , and through the points A , B , C , D draw ( III . 17 ) FG , GH , HK , KF touching the circle ; and because B F E D FG touches the circle ABCD , BOOK FOURTH . 69.
Pagina 71
... ACD and because BD touches the circle , and DC is drawn from the point of contact D , the angle BDC is equal ( III . 32 ) to the angle DAC in the alternate segment of the circle ; to each of these add the angle CDA , then BOOK FOURTH . 71.
... ACD and because BD touches the circle , and DC is drawn from the point of contact D , the angle BDC is equal ( III . 32 ) to the angle DAC in the alternate segment of the circle ; to each of these add the angle CDA , then BOOK FOURTH . 71.
Pagina 73
... ( III . 18 ) to KL ; therefore B K D each of the angles at C is a right angle . For the same reason , the angles at the points B , D are right angles ; and because FCK is a right angle , the square of FK is equal BOOK FOURTH . 73.
... ( III . 18 ) to KL ; therefore B K D each of the angles at C is a right angle . For the same reason , the angles at the points B , D are right angles ; and because FCK is a right angle , the square of FK is equal BOOK FOURTH . 73.
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Elements of Geometry; Containing the First Six Books of Euclid, With Two ... John 1748-1819 Playfair Anteprima non disponibile - 2021 |
Parole e frasi comuni
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