Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of IndivisiblesW. Redmayne, 1714 - 520 σελίδες |
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Σελίδα 42
... say ZE - AE + Eq . a For EZEA + Eq . Z PRO P. IV . A E 3 If a right line Z be cut any - wife into two parts , the Jquare made of the whole line Z is equal both to the fquares made of the fegments 4 , E , and to twice a rectangle made of ...
... say ZE - AE + Eq . a For EZEA + Eq . Z PRO P. IV . A E 3 If a right line Z be cut any - wife into two parts , the Jquare made of the whole line Z is equal both to the fquares made of the fegments 4 , E , and to twice a rectangle made of ...
Σελίδα 75
... say that the line DB fo falling ball touch the circle given . From that point D a let a tangent DF be a 17. 3 . drawn , and from the center E draw ED , EB , EF . Now because DBq b ADC c DFq , there- b byp . = = fore is DB d - DF : But ...
... say that the line DB fo falling ball touch the circle given . From that point D a let a tangent DF be a 17. 3 . drawn , and from the center E draw ED , EB , EF . Now because DBq b ADC c DFq , there- b byp . = = fore is DB d - DF : But ...
Σελίδα 83
... A B x BC may be equal to ACq . From the center A thro ' B , defcribe the circle ABD ; and in this circle b'apply BD b 1.4 . AC , and join AD ; I say ABD is the triangle required . F 2 For c 5. 4 . d 37.3 . e 32.3 . EUCLIDE's Elements .
... A B x BC may be equal to ACq . From the center A thro ' B , defcribe the circle ABD ; and in this circle b'apply BD b 1.4 . AC , and join AD ; I say ABD is the triangle required . F 2 For c 5. 4 . d 37.3 . e 32.3 . EUCLIDE's Elements .
Σελίδα 100
... say that A = B , For let A be greater or less than C.a then is greater o A C Hypothefis . Which is contrary to the 2. Hyp . If C. B : C. A. I say that A - B . For C C let A be B , b then . Which is against the Hypothefis . A B C PROP ...
... say that A = B , For let A be greater or less than C.a then is greater o A C Hypothefis . Which is contrary to the 2. Hyp . If C. B : C. A. I say that A - B . For C C let A be B , b then . Which is against the Hypothefis . A B C PROP ...
Σελίδα 101
... say that A.B : C.D. Take G , H , I the equimultiples of A , C , E ; and K , L , M the equimultiples of B , D , F. Now a because A. B :: E. F , if Ga hyp . K , then after the fame manner I = b 6. def.3 . M. And likewise a because E. F ...
... say that A.B : C.D. Take G , H , I the equimultiples of A , C , E ; and K , L , M the equimultiples of B , D , F. Now a because A. B :: E. F , if Ga hyp . K , then after the fame manner I = b 6. def.3 . M. And likewise a because E. F ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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Δημοφιλή αποσπάσματα
Σελίδα 26 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 406 - ... which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle, between 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...
Σελίδα 269 - A fphere is a folid figure defcribed by the revolution of a i'emicircle about its diameter, which remains unmoved. XV. The axis of a fphere is the fixed ftraight line about which the femicircle revolves. XVI. The centre of a fphere is the fame with that of the femicircle. XVII. The diameter of a fphere is any ftraight line which pafles through the centre, and is terminated both ways by the fuperficies of the fphere.
Σελίδα 2 - The radius of a circle is a right line drawn from the centre to the circumference.
Σελίδα 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.
Σελίδα 269 - ... be less than the other side, an obtuse angled ; and if greater, an acute angled cone. XIX. The axis of a cone is the fixed straight line about which the triangle revolves. XX. The base of a cone is the circle described by that side containing the right angle which revolves. XXI. A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed.
Σελίδα 26 - ... the fum of the remaining angles of the one triangle equal to the fum of the remaining angles of the other. 3 . If one angle in a triangle be right, the other two are equal to a right-angle.
Σελίδα 76 - ... the angular points of the figure about which it is defcribed, each thro' each. III. A rectilineal figure is faid to be infcribed in a circle, when all the angles of the infcribed figure are upon the circumference of the circle.
Σελίδα 77 - ... touch the circumference of the circle. IV A right-lined figure is faid to be defcribed about a circle, when all the fides of the figure which is circumfcribed touch the periphery of the circle V.
Σελίδα 269 - Right Lines that touch one another, and are •not in the fame Superficies: Or, a folid Angle is that which is contained under more than two plane Angles which are not in the fame Superficies, but being all at one Point.