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 - 397 páginas |
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Página 10
... equal to one and the fame Thing , are equal to one another . II . If to equal Things are added equal Things , the Wholes will be equal . III . If from equal Things , equal Things be taken away , the Remainders will be equal . IV . If equal ...
... equal to one and the fame Thing , are equal to one another . II . If to equal Things are added equal Things , the Wholes will be equal . III . If from equal Things , equal Things be taken away , the Remainders will be equal . IV . If equal ...
Página 10
... equal to the whole D G , the Parts whereof DA and D C are equal ; therefore the Remainders Axiom 3. AL , GC are alfo equal t . But it has been demon- ftrated , that BC is equal to CG ; wherefore both AL and BC are each of them equal to ...
... equal to the whole D G , the Parts whereof DA and D C are equal ; therefore the Remainders Axiom 3. AL , GC are alfo equal t . But it has been demon- ftrated , that BC is equal to CG ; wherefore both AL and BC are each of them equal to ...
Página 10
... equal to two Sides of the other , each to each , and the Angle contained by thofe equal Sides in one Triangle equal to the Angle contained by the correfpondent Sides in the other Triangle , then the Bafe of one of the Triangles shall be ...
... equal to two Sides of the other , each to each , and the Angle contained by thofe equal Sides in one Triangle equal to the Angle contained by the correfpondent Sides in the other Triangle , then the Bafe of one of the Triangles shall be ...
Página 10
... equal to them , viz . the Angle ABC equal to the Angle DEF , and the Angle A CB equal to the Angle DFE . Which was to be demonstrated . PROPOSITION V. THEOREM . The Angles at the Bafe of an Ifofceles Triangle are equal between ...
... equal to them , viz . the Angle ABC equal to the Angle DEF , and the Angle A CB equal to the Angle DFE . Which was to be demonstrated . PROPOSITION V. THEOREM . The Angles at the Bafe of an Ifofceles Triangle are equal between ...
Página 10
... equal to the remaining Angles of the other , each to each , which subtend the equal Sides . And fo the An- gle FBC is equal to the Angle GCB : and the Angle BCF equal to the Angle CB G. Therefore because the whole Angle ABG has been proved ...
... equal to the remaining Angles of the other , each to each , which subtend the equal Sides . And fo the An- gle FBC is equal to the Angle GCB : and the Angle BCF equal to the Angle CB G. Therefore because the whole Angle ABG has been proved ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Sin vista previa disponible - 2014 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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.
Página 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...
Página 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.
Página 15 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Página 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.
Página 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.