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 190
... by the Superficies of the Sphere . XVIII . A Cone is a Figure defcribed when one of the Sides of a Right - angled Triangle , containing the the Right Angle , remaining fixed , the Triangle is 190 Book XI . Euclid's ELEMENTS .
... by the Superficies of the Sphere . XVIII . A Cone is a Figure defcribed when one of the Sides of a Right - angled Triangle , containing the the Right Angle , remaining fixed , the Triangle is 190 Book XI . Euclid's ELEMENTS .
Page 191
... Cone is a rectangular Cone ; but if it be lefs , it is an obtufe - angled Cone ; if greater , an acute - angled Cone . XIX . The Axis of a Cone is that fixed Right Line about which the Triangle is moved . XX . The Bafe of a Cone is the ...
... Cone is a rectangular Cone ; but if it be lefs , it is an obtufe - angled Cone ; if greater , an acute - angled Cone . XIX . The Axis of a Cone is that fixed Right Line about which the Triangle is moved . XX . The Bafe of a Cone is the ...
Page 254
... Cone is a third Part of a Cylinder , having the fame Bafe , and an equal Altitude . L ET a Cone have the fame Bafe as a Cylinder , viz . the Circle ABCD , and an Altitude equal to it . I fay the Cone is a third Part of the Cylinder ...
... Cone is a third Part of a Cylinder , having the fame Bafe , and an equal Altitude . L ET a Cone have the fame Bafe as a Cylinder , viz . the Circle ABCD , and an Altitude equal to it . I fay the Cone is a third Part of the Cylinder ...
Page 255
... Cone , it fhall be greater or lefs than triple thereof . First , let it be greater than triple to the Cone , and let the Square ABCD be described in the Circle ABCD , then the Square ABCD is greater than one half of the Circle ABCD ...
... Cone , it fhall be greater or lefs than triple thereof . First , let it be greater than triple to the Cone , and let the Square ABCD be described in the Circle ABCD , then the Square ABCD is greater than one half of the Circle ABCD ...
Page 256
... Cone . But the Prim whofe Bafe is the Polygon AEBF CGDH , and Altitude the fame ; as that of the Cylinder's is * triple of the Pyramid whofe Bafe is the Polygon AE B- FCGDH , and Vertex the same as that of the Cone . And therefore the ...
... Cone . But the Prim whofe Bafe is the Polygon AEBF CGDH , and Altitude the fame ; as that of the Cylinder's is * triple of the Pyramid whofe Bafe is the Polygon AE B- FCGDH , and Vertex the same as that of the Cone . And therefore the ...
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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.