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 245
... DEFH , being equal in Multitude . 1 For fince BX is equal to XC , and AL to LC , XL shall be * parallel to AB , and the Triangle ABC # 2.6 . fimilar to the Triangle LXC . For the fame Reason the Triangle DEF shall be also similar to the ...
... DEFH , being equal in Multitude . 1 For fince BX is equal to XC , and AL to LC , XL shall be * parallel to AB , and the Triangle ABC # 2.6 . fimilar to the Triangle LXC . For the fame Reason the Triangle DEF shall be also similar to the ...
Page 246
... DEFH ; it shall be as the Prism whose Base is the Parallelogram KLXB , and oppofite Base to that the Right Line MO , is to the Prism whose Base is the Triangle LXC ; and oppofite Base to that the Triangle OMN , so is the Prism whose ...
... DEFH ; it shall be as the Prism whose Base is the Parallelogram KLXB , and oppofite Base to that the Right Line MO , is to the Prism whose Base is the Triangle LXC ; and oppofite Base to that the Triangle OMN , so is the Prism whose ...
Page 247
... DEFH . For if it be not so , then it shall be as the Base ABC is to the Base DEF , so is the Pyramid ABCG to fome Solid , greater or less than the Pyramid DE FH . First , let it be to a Solid less , which let be Z , and divide the ...
... DEFH . For if it be not so , then it shall be as the Base ABC is to the Base DEF , so is the Pyramid ABCG to fome Solid , greater or less than the Pyramid DE FH . First , let it be to a Solid less , which let be Z , and divide the ...
Page 248
... DEFH . dy demon- After the fame Manner we demonstrate that the Bafe Strated . DEF to the Base ABC , is not as the ... DEFH . For if this is pof- fible , let it be to the Solid I greater than the Pyra- mid DEFH . Then ( by Inverfion ) ...
... DEFH . dy demon- After the fame Manner we demonstrate that the Bafe Strated . DEF to the Base ABC , is not as the ... DEFH . For if this is pof- fible , let it be to the Solid I greater than the Pyra- mid DEFH . Then ( by Inverfion ) ...
Page 251
... DEFH , has a Pro- portion triplicate of that which BC has to EF . For compleat the solid Parallelepipedons BGML , EHPO ; then because the Pyramid ABCG is fimi- lar to the Pyramid DEFH , the Angle ABC shall be * equal to the Angle DEF ...
... DEFH , has a Pro- portion triplicate of that which BC has to EF . For compleat the solid Parallelepipedons BGML , EHPO ; then because the Pyramid ABCG is fimi- lar to the Pyramid DEFH , the Angle ABC shall be * equal to the Angle DEF ...
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.