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 |
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Page 8
... demonstrated . PROPOSITION V. THEOREM . The Angles at the Base of an Isosceles Triangle are equal between themselves : And if the equal Sides be produced , the Angles under the Base shall be equal between themselves . L ET ABC be an ...
... demonstrated . PROPOSITION V. THEOREM . The Angles at the Base of an Isosceles Triangle are equal between themselves : And if the equal Sides be produced , the Angles under the Base shall be equal between themselves . L ET ABC be an ...
Page 15
... demonstrated . PROPOSITION XIV . THEOREM . If to any Right Line , and Point therein , two Right Lines be drawn from contrary Parts , making the adjacent Angles , both together , equal to two Right Angles , the said two Right Lines will ...
... demonstrated . PROPOSITION XIV . THEOREM . If to any Right Line , and Point therein , two Right Lines be drawn from contrary Parts , making the adjacent Angles , both together , equal to two Right Angles , the said two Right Lines will ...
Page 23
... demonstrated . PROPOSITION XXV . / THEOREM . If two Triangles have two Sides of the one equal to two Sides of the other , each to each , and the Base of the one greater than the Base of the other ; they shall also have the Angles ...
... demonstrated . PROPOSITION XXV . / THEOREM . If two Triangles have two Sides of the one equal to two Sides of the other , each to each , and the Base of the one greater than the Base of the other ; they shall also have the Angles ...
Page 26
... demonstrated . PROPOSITION XXVII . THEOREM . If a Right Line , falling upon two Right Lines , makes the alternate Angles equal between them- Selves , the two Right Lines shail be parallel . L ET the Right Line EF , falling upon two ...
... demonstrated . PROPOSITION XXVII . THEOREM . If a Right Line , falling upon two Right Lines , makes the alternate Angles equal between them- Selves , the two Right Lines shail be parallel . L ET the Right Line EF , falling upon two ...
Page 28
... , on the Same Side , and the inward Angles on the fame Side together equal to two Right Angles ; which was to be demonstrated . PRO- PROPOSITION XXX . THEOREM . Right Lines parallel to one 28 Euclid's ELEMENTS . Book I.
... , on the Same Side , and the inward Angles on the fame Side together equal to two Right Angles ; which was to be demonstrated . PRO- PROPOSITION XXX . THEOREM . Right Lines parallel to one 28 Euclid's ELEMENTS . Book I.
Common terms and phrases
alfo alſo equal Altitude Angle ABC Angle BAC Bafe becauſe biſected Center Circle ABCD Circle EFGH Circumference Cofine Cone conſequently Coroll Cylinder demonftrated deſcribed Diameter Diſtance drawn thro equal Angles equiangular equilateral Equimultiples faid fame Altitude fame Plane fame Reaſon fimilar fince firſt folid Parallelepipedon fore fubtending given Right Line Gnomon greater join leſs likewiſe Logarithm Magnitudes Meaſure Number oppoſite parallel Parallelogram perpendicular Polygon Priſms Prop PROPOSITION Pyramid Pyramid ABCG Quadrant Radius Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line AC Right-lined Figure ſame ſame Multiple ſay ſecond Segment ſhall be equal Side BC ſince Sine Solid ſome Sphere ſtand Subtangent THEOREM thereof theſe thoſe three Right Lines Triangle ABC Unity Vertex the Point Wherefore whole
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 11 - ... 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 17 - 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.