## 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 Plain and Spherical Trigonometry : with a Preface ... |

### From inside the book

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**one equal to two Angles of the other , each to each , and**one Side of the one equal to one Side of the other , either the Side lying between the equal Angles , or which fubtends one of the equal Angles ; the remaining Sides of the one ... Page 111

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**one equal to two Angles of the other , each to each , and**one Side of the one equal to one Side of the other , viz . the common Side FC ; where- fore they fhall have the other Sides of the one equal † 26. 1 . to the other Sides of the ... Page 194

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**one equal to two Angles of the other , each to each , and**one Side A E equal to one Side EB , viz . those that are at the equal Angles ; and fo the other Sides of the one , will be + equal to the other Sides of the other . Therefore G H ... Page 230

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**one equal to two Angles of the other , each to each , and**one Side of the one equal to one Side of the other , viz . that which is fubtended by one of the equal Angles ; that is , the Side HA equal to DM ; and fo the other 26.1 . Sides ...### Common terms and phrases

alfo equal alſo Angle ABC Angle BAC Baſe becauſe bifected Center Circle ABCD Circle EFGH Circumference Cofine Cone confequently contain'd Coroll Cylinder defcrib'd defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular equilateral Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft firſt folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number paffing thro Parallelogram perpendicular Polygon Prifm Priſms Prop PROPOSITION Pyramid Quadrant Ratio Rectangle remaining Angle Right Angles Right Line A B Right Line AB Right-lin'd Figure Right-lin❜d Segment ſhall Sine Solid Sphere Subtangent thefe THEOREM theſe thofe Triangle ABC triplicate Proportion Unity Vertex the Point Wherefore whofe Bafe whole

### Popular passages

Page 190 - 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 160 - 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 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.

Page 152 - ... therefore the angle DFG is equal to the angle DFE, and the angle at G to the angle at E : but the angle DFG is equal to the angle ACB...

Page 100 - About a given circle to describe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to describe a triangle about the circle ABC equiangular to the triangle DEF.

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 210 - 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 229 - 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.

Page 164 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.

Page 93 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.