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 46
... divided into any Number of Parts ; the Rett- angle comprehended under the whole , and di- vided Line , fhall be equal to all the Rectangles contained under the whole Line , and the feveral Segments of the divided Line . L ' ET A and BC ...
... divided into any Number of Parts ; the Rett- angle comprehended under the whole , and di- vided Line , fhall be equal to all the Rectangles contained under the whole Line , and the feveral Segments of the divided Line . L ' ET A and BC ...
Page 47
... divided , the Rectangles contained under the whole Line , and each of the Segments , or Parts , are equal to the Square of the whole Line . ET the Right Line A B be any how divided in the Point C. I fay , the Rectangle contained under ...
... divided , the Rectangles contained under the whole Line , and each of the Segments , or Parts , are equal to the Square of the whole Line . ET the Right Line A B be any how divided in the Point C. I fay , the Rectangle contained under ...
Page 50
... with the Square that is made of the intermediate Distance , is equal to the Square made of half the Line ; which was to be demonstrated , PRO- PROPOSITION VI THEOREM . If a Right Line be divided 50 Euclid's ELEMENTS . Book II .
... with the Square that is made of the intermediate Distance , is equal to the Square made of half the Line ; which was to be demonstrated , PRO- PROPOSITION VI THEOREM . If a Right Line be divided 50 Euclid's ELEMENTS . Book II .
Page 51
... divided into two equal Parts , and another Right Line be added directly to the fame , the Rectangle contained under the Line , com- pounded of the whole and added Line , ( taken as one Line , ) and the added Line , together with the ...
... divided into two equal Parts , and another Right Line be added directly to the fame , the Rectangle contained under the Line , com- pounded of the whole and added Line , ( taken as one Line , ) and the added Line , together with the ...
Page 61
... divided into two equal Parts in G , and into two unequal ones in E , the Rectangle under BE and EF , together with the Square of GE , fhall be equal to the Square of GF . 15 of this . But GF is equal to GH . Therefore the Rectangle ...
... divided into two equal Parts in G , and into two unequal ones in E , the Rectangle under BE and EF , together with the Square of GE , fhall be equal to the Square of GF . 15 of this . But GF is equal to GH . Therefore the Rectangle ...
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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.