## 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 ... |

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Page 190

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**Prism**is a folid Figure contained under Planes , whereof the two opposite are equal , fimilar , and pa- rallel , and the others Parallelograms . XIV . A Sphere is a folid Figure , made when the Dia- meter of a Semicircle , remaining at ... Page 219

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**Prism**contained by the two Triangles CGF , ADE , and the three Parallelograms GE , AC , CE , is equal to the**Prism**contained under the two Triangles CFB , DEH , and the three Parallelograms CH , BE , CE ; for they are contained under ... Page 220

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**Prism**contained under the two Triangles AFG , DEC , and the three Parallelograms AD , DG , GC , is equal to the**Prism**contained under the two Trian- gles LMN , HBK , and the three Parallelograms BM , NH , BN . Let the common Solid ... Page 236

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**Prisms**of equal Altitude . The Base of one of which is the Parallelogram AF , and that of the other , the Triangle GHK , and let the Parallelogram AF be double to the Triangle GHK . I say the**Prism**A B CDEF is equal to the**Prism**GHKLMN ... Page 236

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**Prism**GH KLMN . Wherefore , if there be two Prifms having equal Altitudes , the Bafe of one of which is a Parallelo- gram , and that of the other a Triangle , and if the Pa- rallelogram be double to the Triangle , the faid**Prisms**fhall ...### Common terms and phrases

alfo alſo equal Altitude Angle ABC Angle BAC Angle BCD Bafe Baſe BC becauſe biſected Center Circle ABCD Circle EFGH Circumference Cofine Cone confequently contain'd Coroll Cylinder defcrib'd DEFH demonftrated deſcribed Diameter Diſtance drawn thro equal Angles equiangular equilateral Equimultiples fame Multiple fame Reaſon fimilar fince firſt folid Parallelepipedon fore fubtending given Right Line greater join leffer leſs likewife Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Plane Polygon Priſms Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line AC Right-lin'd Figure ſame ſay ſecond Segment Semicircle ſhall be equal Sine ſome Sphere ſtand Subtangent THEOREM theſe thoſe Triangle ABC Unity Vertex the Point Wherefore whole

### Popular passages

Page 192 - 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 162 - 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 154 - ... 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 212 - 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 233 - 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 166 - 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 95 - 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.