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 5
... proved to be equal to AB ; there- fore both CA and CB are each equal to AB . But things equal to one and the fame thing , are equal be- tween themselves , and confequently CA is equal to CB ; therefore the three Sides CA , AB , BC , are ...
... proved to be equal to AB ; there- fore both CA and CB are each equal to AB . But things equal to one and the fame thing , are equal be- tween themselves , and confequently CA is equal to CB ; therefore the three Sides CA , AB , BC , are ...
Page 8
... proved to be equal to GB ; therefore the two Sides BF , FC , are equal to the two Sides CG , GB , each to each , and the Angle BFC equal to the Angle CGB ; but they have a common Bafe BC . Therefore alfo the Tri- angle BFC will be equal ...
... proved to be equal to GB ; therefore the two Sides BF , FC , are equal to the two Sides CG , GB , each to each , and the Angle BFC equal to the Angle CGB ; but they have a common Bafe BC . Therefore alfo the Tri- angle BFC will be equal ...
Page 9
... proved equal to the whole Angle ACF , and the Part C B G equal to BCF , the re- maining Angle ABC will be equal to the remaining • Ax . 3 . Angle ACB ; but these are the Angles at the Bafe of the Triangle ABC . It hath likewife been proved ...
... proved equal to the whole Angle ACF , and the Part C B G equal to BCF , the re- maining Angle ABC will be equal to the remaining • Ax . 3 . Angle ACB ; but these are the Angles at the Bafe of the Triangle ABC . It hath likewife been proved ...
Page 10
... proved to be much greater , which is impoffible . Therefore on the fame Right Line cannot be conftituted two Right Lines equal to two other right Lines , each to each , at different Points , on the fame Side , and having the fame Ends ...
... proved to be much greater , which is impoffible . Therefore on the fame Right Line cannot be conftituted two Right Lines equal to two other right Lines , each to each , at different Points , on the fame Side , and having the fame Ends ...
Page 11
... proved to be otherwife ; therefore it is impoffible for the 7 of this . Sides BA , AC , not to co - incide with the Sides ED , DF , if the Bafe B C co - incides with the Base EF ; wherefore they will co - incide , and confequently the ...
... proved to be otherwife ; therefore it is impoffible for the 7 of this . Sides BA , AC , not to co - incide with the Sides ED , DF , if the Bafe B C co - incides with the Base EF ; wherefore they will co - incide , and confequently the ...
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.