Euclid's Elements of Geometry: From the Latin Translation of Commandine. To which is Added, a Treatise of the Nature and Arithmetic of Logarithms; Likewise Another of the Elements of Plane and Spherical Trigonometry; with a Preface, Shewing the Usefulness and Excellency of this Work |
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Page 9
... fore in English , nor any other which may properly be said to contain the Demonstra- tions laid down by Euclid himself , I do not doubt but the Publication of this Edi- tion will be acceptable , as well as fervice- able . Such Errors ...
... fore in English , nor any other which may properly be said to contain the Demonstra- tions laid down by Euclid himself , I do not doubt but the Publication of this Edi- tion will be acceptable , as well as fervice- able . Such Errors ...
Page 11
... but they have a common Base BC . There- fore also the Triangle BFC will be equal to the * 4 of this . Triangle CGB * , and the remaining Angles of the one equal 1 9 equal to the remaining Angles of the other , 8 Euclid's ELEMENTS . Book I.
... but they have a common Base BC . There- fore also the Triangle BFC will be equal to the * 4 of this . Triangle CGB * , and the remaining Angles of the one equal 1 9 equal to the remaining Angles of the other , 8 Euclid's ELEMENTS . Book I.
Page 17
... fore the Angle A CD is greater than the Angle BAE . After the same manner , if the Right Line BC be bisected , we demonstrate that the Angle BCG , and consequently its equal , the Angle ACD * , is greater 15 of this . than the Angle ABC ...
... fore the Angle A CD is greater than the Angle BAE . After the same manner , if the Right Line BC be bisected , we demonstrate that the Angle BCG , and consequently its equal , the Angle ACD * , is greater 15 of this . than the Angle ABC ...
Page 18
... fore the Angle BAC is neceffarily greater than the Angle EDF . If , therefore , 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 ather ; they ...
... fore the Angle BAC is neceffarily greater than the Angle EDF . If , therefore , 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 ather ; they ...
Page 20
... fore it is equal to it . But A B is also equal to DE . Wherefore the two Sides A B , BC , are equal to the two Sides DE , E F , each to each ; and they contain equal Angles . And so the Base A C is equal to the Bafe D F , the Triangle ...
... fore it is equal to it . But A B is also equal to DE . Wherefore the two Sides A B , BC , are equal to the two Sides DE , E F , each to each ; and they contain equal Angles . And so the Base A C is equal to the Bafe D F , the Triangle ...
Other editions - View all
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill No preview available - 2018 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill No preview available - 2017 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill No preview available - 2015 |
Common terms and phrases
alfo alſo equal Altitude Angle ABC Angle BAC Bafe becauſe biſected Centre Circle ABCD Circle EFGH Circumference Cofine Cone conſequently Coroll Cylinder demonftrated deſcribed Diameter Diſtance drawn thro equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fimilar fince firſt folid Parallelepipedon fore fubtending given Right Line greater join leſs likewiſe Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Polygon Priſm Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure ſame ſay ſecond Segment Semicircle ſhall be equal Sides ſince Sine ſome Sphere Square ſtand Subtangent THEOREM thereof theſe thoſe three Right Lines tiple Triangle ABC Unity Vertex the Point Wherefore whole whoſe Baſe
Popular passages
Page 193 - 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 168 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...
Page 18 - ... 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 52 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 121 - GB is equal to E, and HD to F; GB and HD together are equal to E and F together : wherefore as many magnitudes as...
Page 213 - CD; therefore AC is a parallelogram. In like manner, it may be proved that each of the figures CE, FG, GB, BF, AE, is a parallelogram...
Page 194 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.
Page 159 - And because HE is parallel to KC, one of the sides of the triangle DKC, as CE to ED, so is...
Page 205 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. V. The inclination of a straight line to a plane...