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 10
... proved to be equal to AB ; there- fore both CA and CB are each equal to AB . But Things equal to one and the fame Thing , are equal between themselves , and confequently CA is equal to CB ; therefore the three Sides CA , A B , B C , are ...
... proved to be equal to AB ; there- fore both CA and CB are each equal to AB . But Things equal to one and the fame Thing , are equal between themselves , and confequently CA is equal to CB ; therefore the three Sides CA , A B , B C , are ...
Page 10
... proved to be equal to GB ; therefore the two Sides BF , FC , are equal to the two Sides CG , GB , each to each , and the Angle B F C equal to the Angle CGB ; but they have a common Bafe BC . There¬ fore alfo the Triangle BFC will be ...
... proved to be equal to GB ; therefore the two Sides BF , FC , are equal to the two Sides CG , GB , each to each , and the Angle B F C equal to the Angle CGB ; but they have a common Bafe BC . There¬ fore alfo the Triangle BFC will be ...
Page 10
... proved equal to the whole Angle ACF , and the Part CBG equal to BCF , the remaining Angle A B C will be equal to * Ax . 3 . the remaining Angle A CB ; but these are the Angles at the Base of the Triangle ABC . It hath likewise been proved ...
... proved equal to the whole Angle ACF , and the Part CBG equal to BCF , the remaining Angle A B C will be equal to * Ax . 3 . the remaining Angle A CB ; but these are the Angles at the Base of the Triangle ABC . It hath likewise been proved ...
Page 10
... proved to be much greater , which is impoffible . Therefore on the fame Right Line cannot be conftituted two Right Lines equal to two other Right Lines , each to each , at different Points , on the fame Side , and having the fame Ends ...
... proved to be much greater , which is impoffible . Therefore on the fame Right Line cannot be conftituted two Right Lines equal to two other Right Lines , each to each , at different Points , on the fame Side , and having the fame Ends ...
Page 10
... proved to be otherwise * ; therefore it is impoffible for the * Sides BA , AC , not to co - incide with the Sides ED , DF , if the Bafe BC co - incides with the Bafe EF ; wherefore they will co - incide , and confequently the Angle BAC ...
... proved to be otherwise * ; therefore it is impoffible for the * Sides BA , AC , not to co - incide with the Sides ED , DF , if the Bafe BC co - incides with the Bafe EF ; wherefore they will co - incide , and confequently the Angle BAC ...
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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.