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 117
... Multiple is a Magnitude of a Magnitude , the greater of the leffer , when the leffer measures the greater . III . Ratio , is a certain mutual Habitude of Mag- nitudes of the fame kind , according to Quantity . IV . Magnitudes are faid ...
... Multiple is a Magnitude of a Magnitude , the greater of the leffer , when the leffer measures the greater . III . Ratio , is a certain mutual Habitude of Mag- nitudes of the fame kind , according to Quantity . IV . Magnitudes are faid ...
Page 118
... Multiple of the first be greater than the Multiple of the second , and also the Multiple of the third greater than the Multiple of the fourth : Or , if the Multiple of the first be equal to the Multiple of the second ; and also the Multiple ...
... Multiple of the first be greater than the Multiple of the second , and also the Multiple of the third greater than the Multiple of the fourth : Or , if the Multiple of the first be equal to the Multiple of the second ; and also the Multiple ...
Page 119
... Multiple of A : And fo ( by Cafe 1. ) D will be the fame Multiple of C , and accordingly C fhall be the fame Part of the Magnitude D , as A is of B. W.W.D. Thirdly , Let A be equal to any Number of what- foever Parts of B. I fay , C is ...
... Multiple of A : And fo ( by Cafe 1. ) D will be the fame Multiple of C , and accordingly C fhall be the fame Part of the Magnitude D , as A is of B. W.W.D. Thirdly , Let A be equal to any Number of what- foever Parts of B. I fay , C is ...
Page 120
... Multiple of the firft exceeds the Multiple of the fecond , but the Multiple of the third does not exceed the Mul- tiple of the fourth ; then the first to the fecond is faid to have a greater Proportion than the third to the fourth ...
... Multiple of the firft exceeds the Multiple of the fecond , but the Multiple of the third does not exceed the Mul- tiple of the fourth ; then the first to the fecond is faid to have a greater Proportion than the third to the fourth ...
Page 125
... Multiple of A , as L is of L F C D H N C. For the fame Reason , M is the fame Multiple of B , as N is of D. And fince A is to B , as C is to D , and K and L are Equimul- tiples of A and C ; and alfo M and N Equimultiples of B and D. If ...
... Multiple of A , as L is of L F C D H N C. For the fame Reason , M is the fame Multiple of B , as N is of D. And fince A is to B , as C is to D , and K and L are Equimul- tiples of A and C ; and alfo M and N Equimultiples of B and D. If ...
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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.