Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To which is Added, A Treatise of the Nature of Arithmetic of Logarithms; Likewise Another of the Elements of Plain and Spherical Trigonometry; with a Preface...Tho. Woodward at the Half-Moon, between the Two Temple-Gates in Fleet-street; and sold by, 1733 - 397 Seiten |
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Seite 62
... to the Square of EH . And fo there is a Square made equal to the given Right- lined Figure A , viz . the Square of EH ; which was to be done . The END of the SECOND Book . EUCLID's Book 2 . B DEC A C B A Pag 62 Book II . Euclid's ELEMENTS .
... to the Square of EH . And fo there is a Square made equal to the given Right- lined Figure A , viz . the Square of EH ; which was to be done . The END of the SECOND Book . EUCLID's Book 2 . B DEC A C B A Pag 62 Book II . Euclid's ELEMENTS .
Seite 105
... second Figure , and join AF . Then we prove , as before , that the Point F is the Center of a Circle defcribed about the Triangle ABC . Laftly , let the Right Lines DF , EF , meet one another again in the Point F , without the Triangle ...
... second Figure , and join AF . Then we prove , as before , that the Point F is the Center of a Circle defcribed about the Triangle ABC . Laftly , let the Right Lines DF , EF , meet one another again in the Point F , without the Triangle ...
Seite 118
... second and fourth . And if the Multiple of the first be greater than the Multiple of the second , and also the Multiple of the third greater than the Multiple of the fourth : Or , if the Multiple of the first be equal to the Multiple of ...
... second and fourth . And if the Multiple of the first be greater than the Multiple of the second , and also the Multiple of the third greater than the Multiple of the fourth : Or , if the Multiple of the first be equal to the Multiple of ...
Seite 119
... second and fourth , viz . 4A , 5B , 4C , 5D . 5B , 5D , and ( by the Definition ) if 4A is equal to 5B ; then 4C is equal to 5D . But 4A has been proved equal to 5B , and fo 4C fhall be equal to 5D , and Cequal to D. W.W.D. n - And ...
... second and fourth , viz . 4A , 5B , 4C , 5D . 5B , 5D , and ( by the Definition ) if 4A is equal to 5B ; then 4C is equal to 5D . But 4A has been proved equal to 5B , and fo 4C fhall be equal to 5D , and Cequal to D. W.W.D. n - And ...
Seite 174
... Second B to the third C , and of the Ratio of the third C to the fourth D. For in three Right Lines A , C , and D , the Ratio of A to D , is equal to the Ratio's compounded of the Ra- tio's of A to C , and of C to D ; and it has been ...
... Second B to the third C , and of the Ratio of the third C to the fourth D. For in three Right Lines A , C , and D , the Ratio of A to D , is equal to the Ratio's compounded of the Ra- tio's of A to C , and of C to D ; and it has been ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2014 |
Häufige Begriffe und Wortgruppen
adjacent Angles alfo equal alſo Angle ABC Angle BAC Bafe Baſe becauſe bifected Center Circle ABCD Circumference Cofine Cone confequently Coroll Cylinder defcribed demonftrated Diameter Diſtance drawn thro EFGH equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fecond fhall be equal fimilar fince firft firſt folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs leſs likewife Logarithm Magnitudes Meaſure Number Parallelogram perpendicular Polygon Priſms Prop PROPOSITION Pyramid Pyramid ABCG Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line AC Right-lined Figure Segment ſhall Sine Solid Sphere Subtangent themſelves THEOREM theſe thofe thoſe Triangle ABC Unity Vertex the Point Wherefore whofe Bafe whole whoſe Baſe
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Seite 66 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 163 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Seite 112 - And in like manner it may be shown that each of the angles KHG, HGM, GML is equal to the angle HKL or KLM ; therefore the five angles GHK, HKL, KLM, LMG, MGH...
Seite 90 - IN a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 22 - ... sides equal to them of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB...
Seite 10 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.
Seite 15 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Seite 33 - ... therefore their other sides are equal, each to each, and the third angle of the one to the third angle of the other, (i.
Seite 113 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.