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 - Geometry - 397 pages |
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Page 35
... EFGH is equal to the fame Parallelo gram EBCH . Therefore the Parallelogram ABCD fhall be equal to the Parallelogram EFGH . And fo Parallelograms conftituted upon equal Bafes , and be- tween the fame Parallels , are equal between them ...
... EFGH is equal to the fame Parallelo gram EBCH . Therefore the Parallelogram ABCD fhall be equal to the Parallelogram EFGH . And fo Parallelograms conftituted upon equal Bafes , and be- tween the fame Parallels , are equal between them ...
Page 239
... EFGH , be Circles , whofe Dia- meters are BD , FH . I fay , as the Square of BD is to the Square of FH , fo the Circle ABCD to the Circle EFGH . For * 41. 1 . For if it be not fo Book XII . Euclid's ELEMENTS . 239.
... EFGH , be Circles , whofe Dia- meters are BD , FH . I fay , as the Square of BD is to the Square of FH , fo the Circle ABCD to the Circle EFGH . For * 41. 1 . For if it be not fo Book XII . Euclid's ELEMENTS . 239.
Page 240
... EFGH . First let it be to a Space S , lefs than the Circle EFGH , and let the Square EFGH be described therein . * This Square EFGH will be greater than half the Circle EFGH ; because if we draw Tangents to the Circle thro ' the Points ...
... EFGH . First let it be to a Space S , lefs than the Circle EFGH , and let the Square EFGH be described therein . * This Square EFGH will be greater than half the Circle EFGH ; because if we draw Tangents to the Circle thro ' the Points ...
Page 241
... E F G H , the Space fhall be to the Circle ABCD , as the Circle EFGH is to fome Space less than the Circle ABCD . Therefore , as the Square of FH is to the Square of BD , fo is the Circle * 11. 5 . EF GH to fome Space lefs than the ...
... E F G H , the Space fhall be to the Circle ABCD , as the Circle EFGH is to fome Space less than the Circle ABCD . Therefore , as the Square of FH is to the Square of BD , fo is the Circle * 11. 5 . EF GH to fome Space lefs than the ...
Page 258
... EFGH , fo is the Cone AL to some Solid either lefs or greater than the Cone EN . First , let it be to the Solid X ... EFGH be defcribed in the Circle EFGH , which Square is greater than one half of the Circle , and erect a Pyramid upon ...
... EFGH , fo is the Cone AL to some Solid either lefs or greater than the Cone EN . First , let it be to the Solid X ... EFGH be defcribed in the Circle EFGH , which Square is greater than one half of the Circle , and erect a Pyramid upon ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill No preview available - 2014 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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...
Page 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.
Page 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...
Page 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.
Page 15 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Page 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.
Page 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.