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
... wherefore both AL and BC are each of them equal to CG . But Things that are equal to one and the fame Thing , are ... wherefore AE is likewife equal ‡ Axiom 1. to C ‡ . And fo there is cut off from A B the greater of two given Right ...
... wherefore both AL and BC are each of them equal to CG . But Things that are equal to one and the fame Thing , are ... wherefore AE is likewife equal ‡ Axiom 1. to C ‡ . And fo there is cut off from A B the greater of two given Right ...
Page 13
... Wherefore when a Right Line , ftanding upon another Right Line , makes Angles , thefe fhall be either two Right Angles , or together equal to two Right Angles ; which was to be demonftrated . PROPOSITION XIV . THEOREM . If to any Right ...
... Wherefore when a Right Line , ftanding upon another Right Line , makes Angles , thefe fhall be either two Right Angles , or together equal to two Right Angles ; which was to be demonftrated . PROPOSITION XIV . THEOREM . If to any Right ...
Page 19
... Wherefore AC is greater than AB . Therefore the greater Angle of every Triangle fubtends the greater Side ; which was to be demonftrated . PROPOSITION XX . THEOREM . Two Sides of any Triangle , bowfoever taken , are together greater ...
... Wherefore AC is greater than AB . Therefore the greater Angle of every Triangle fubtends the greater Side ; which was to be demonftrated . PROPOSITION XX . THEOREM . Two Sides of any Triangle , bowfoever taken , are together greater ...
Page 28
... Wherefore it is ne ceffarily equal to it . 1.25 of this . But the Angle AGH ist equal to the Angle EGB : Therefore EGB is alfo equal to GHD Now add the common Angle BGH , and then EGB , BGH , together , are equal to BGH , GHD , together ...
... Wherefore it is ne ceffarily equal to it . 1.25 of this . But the Angle AGH ist equal to the Angle EGB : Therefore EGB is alfo equal to GHD Now add the common Angle BGH , and then EGB , BGH , together , are equal to BGH , GHD , together ...
Page 30
... Wherefore the whole outward Angle ACD is equal to both the inward and oppo- fite Angles BAC , ABC . And if the Angle ACB , which is common , be added , the two Angles ACD , ACB , are equal to the three Angles ABC , BAC , 13 of this ...
... Wherefore the whole outward Angle ACD is equal to both the inward and oppo- fite Angles BAC , ABC . And if the Angle ACB , which is common , be added , the two Angles ACD , ACB , are equal to the three Angles ABC , BAC , 13 of this ...
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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.