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
... touch each other , but do not both lie in the fame Right Line . IX . If the Lines containing the Angle be Right ones , then the Angle is call'd a Right - lin'd Angle . X. When X. When a Right Line , standing on another Right.
... touch each other , but do not both lie in the fame Right Line . IX . If the Lines containing the Angle be Right ones , then the Angle is call'd a Right - lin'd Angle . X. When X. When a Right Line , standing on another Right.
Page 63
... touch a Circle when touching the fame , and being produced , does not cut it . II . Circles are faid to touch each other , which Touching do not cut one another . V. Right Lines in a Circle are faid to be equally diftant from the Center ...
... touch a Circle when touching the fame , and being produced , does not cut it . II . Circles are faid to touch each other , which Touching do not cut one another . V. Right Lines in a Circle are faid to be equally diftant from the Center ...
Page 65
... fhall fall within the Circle ; which was to be demonftrated . Coroll . Hence if a Right Line touches a Circle , it will touch it in one Point only . PRO- I PROPOSITION III . THEOREM . If in a Circle Book III . Euclid's ELEMENTS . 65.
... fhall fall within the Circle ; which was to be demonftrated . Coroll . Hence if a Right Line touches a Circle , it will touch it in one Point only . PRO- I PROPOSITION III . THEOREM . If in a Circle Book III . Euclid's ELEMENTS . 65.
Page 68
... touch one another inwardly , they will not have one and the fame Center . ET two Circles ABC , CDE , touch one an- other inwardly in the Point C. I fay , they will not have one and the fame Center . } For if they have , let it be F ...
... touch one another inwardly , they will not have one and the fame Center . ET two Circles ABC , CDE , touch one an- other inwardly in the Point C. I fay , they will not have one and the fame Center . } For if they have , let it be F ...
Page 74
... cutting each other , which is abfurd . Wherefore a Circle cannot cut a Circle in more than two Points ; which was to be de- monftrated . PRO- PROPOSITION XI . THEOREM . If two Circles touch each 74 Book III . Euclid's ELEMENTS .
... cutting each other , which is abfurd . Wherefore a Circle cannot cut a Circle in more than two Points ; which was to be de- monftrated . PRO- PROPOSITION XI . THEOREM . If two Circles touch each 74 Book III . Euclid's ELEMENTS .
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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.