The Elements of Euclid: With Select Theorems Out of Archimedes |
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Page 2
... because he was not yet about to treat concerning it . But left any one fhould want the Definition thereof , take it here thus : A Body is a Magnitude long , broad and deep . A Body therefore hath three Dimenfions , a Surface two , a ...
... because he was not yet about to treat concerning it . But left any one fhould want the Definition thereof , take it here thus : A Body is a Magnitude long , broad and deep . A Body therefore hath three Dimenfions , a Surface two , a ...
Page 10
... because the Angles B and C are equal to thofe F and I , when the Side FI is laid upon the Side BC : FL ( b ) will fall exact- ly upon BA , and IL upon CA. Therefore the Point L will fall upon the Point A ( for if it fall without A , the ...
... because the Angles B and C are equal to thofe F and I , when the Side FI is laid upon the Side BC : FL ( b ) will fall exact- ly upon BA , and IL upon CA. Therefore the Point L will fall upon the Point A ( for if it fall without A , the ...
Page 11
... because therefore in the Triangles ABC , cba , one Side A'C is equal to one Side ( ca ) and the Angle A is equal to the Angle c , and the Angle C equal to the Angle a , all the other Things fhall be likewife ( a ) equal , and ...
... because therefore in the Triangles ABC , cba , one Side A'C is equal to one Side ( ca ) and the Angle A is equal to the Angle c , and the Angle C equal to the Angle a , all the other Things fhall be likewife ( a ) equal , and ...
Page 14
... because the unequal Angles CAB , FAB poffefs the fame Place which the two right ones CAL , LAF do , and agree ( g ) Per Axi . to them , they are equal ( g ) to them . 2. E.D. 7 . Fig . 37 . Fig . 36 . I. Corollaries . I IN the fame ...
... because the unequal Angles CAB , FAB poffefs the fame Place which the two right ones CAL , LAF do , and agree ( g ) Per Axi . to them , they are equal ( g ) to them . 2. E.D. 7 . Fig . 37 . Fig . 36 . I. Corollaries . I IN the fame ...
Page 15
... because B A ftands upon the right Line L F , the Angles LA B , FAB are ( c ) equal to two right ones : ( c ) Per 13.1 . And because FA ftands upon the right Line BC , the Angles FAC , FAB are alfo equal ( d ) to two right ( d ) By the ...
... because B A ftands upon the right Line L F , the Angles LA B , FAB are ( c ) equal to two right ones : ( c ) Per 13.1 . And because FA ftands upon the right Line BC , the Angles FAC , FAB are alfo equal ( d ) to two right ( d ) By the ...
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The Elements of Euclid: With Select Theorems Out of Archimedes Archimedes,André Tacquet,Euclid No preview available - 2015 |
Common terms and phrases
alfo alfo equal alſo Altitude Arch Archimedes Axis Bafe Baſe becauſe betwixt themſelves bifected Centre Circum circumfcrib'd Circumference confequently Conftruction conical Superficies conical Surfaces contain'd Coroll Corollary Cylinder defcrib'd defcribe demonftrated Diameter double drawn thro equal Angles equilateral Cone equilateral Triangle Euclid faid fame manner fcrib'd fecond felf fhall be equal fhew fhew'd Figure firft firſt folid Angle fome fore foregoing four right ftand fuppos'd given right Line greater hath Height Hypothefis infcrib'd infcribed Interfections leffer lefs likewife Line BC manifeft Mathematicks mean Proportional betwixt Meaſure Number oppofite pafs thro parallel Parallelepiped Parallelogram Pentagon perpendicular Plane Point Polygon Prifm Priſms Proclus produc'd PROP Propofition Pyramids Radius Rectangle right Angle right Line Scholium Segment Semidiameter Solid Sphere Square thefe Theorem theſe Thing thofe unto whatſoever whofe whole Superficies
Popular passages
Page 21 - 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.
Page xviii - A Scheme of the Solar Syftem, with the orbits of the planets and comets belonging thereto, defcribed from Dr. Halley's accurate Table of Comets, Philofoph.
Page xviii - Difcovery of Divine Truth : And of the Degree of Evidence that , ought to be expected in Divine Matters, 8vo.
Page xviii - Syllem briefly demonftrated. IV. Certain Obfervations drawn from that Syftem. V. Probable Conjectures of the Nature and Ufes of the feveral celeftial Bodies contain'd in the fame Syflem.
Page xviii - DHcovery of divine Truth, and of the degree of Evidence that ought to be expected in divine Matters. By William WbiftvK, MA Ibmetime Profeffor of the Mathematicks in the Univerfity of Cambridge.
Page 11 - Because the angle A is equal to the angle C, and the angle...
Page xviii - Bodies contained in the fame Syftem. VI.' Important Principles of NATURAL RELIGION Demonftrated from the foregoing Obfervations.
Page xix - How great a Geometrician art thou, O Lord! For while this Science has no Bounds, while there is for ever room for the Discovery of New Theorems, even by Human Faculties; Thou art acquainted with them all at one View, without any Chain of Consequences, without any Fatigue of Demonstrations.
Page 211 - Side next to the Diameter : and let the right Lines BH, CG, DF, join the Angles which are equally diftant from A. I fay that the...
Page 221 - Axis, is alfo given j it is manifeft that each of the Segments become known. Now both the foregoing, and all the reft of the Theorems which follow...