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 ...T. Woodward, 1723 - 364 páginas |
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Página 7
... Angle contained by thofe equal Sides in one Triangle equal to the Angle ... remaining Angles of the other , each to each , which fubtend the equal Sides ... Angle BAC equal to the Angle EDF . I fay , that the Bafe BC is equal to the Bafe ...
... Angle contained by thofe equal Sides in one Triangle equal to the Angle ... remaining Angles of the other , each to each , which fubtend the equal Sides ... Angle BAC equal to the Angle EDF . I fay , that the Bafe BC is equal to the Bafe ...
Página 8
... remaining Angles + 4x . 8. will co - incide with the remaining Angles † , and will be equal to them , viz . the Angle ABC equal to the Angle DEF , and the Angle ACB equal to the An- gle DFE . Which was to be demonstrated . PROPOSITION ...
... remaining Angles + 4x . 8. will co - incide with the remaining Angles † , and will be equal to them , viz . the Angle ABC equal to the Angle DEF , and the Angle ACB equal to the An- gle DFE . Which was to be demonstrated . PROPOSITION ...
Página 9
... remaining • Ax . 3 . Angle ACB ; but these are the Angles at the Bafe of the Triangle ABC . It hath likewife been proved that the Angles FBC , GC B , under the Bafe , are equal ; therefore the Angles at the Bafe of Ifofceles Triangles ...
... remaining • Ax . 3 . Angle ACB ; but these are the Angles at the Bafe of the Triangle ABC . It hath likewife been proved that the Angles FBC , GC B , under the Bafe , are equal ; therefore the Angles at the Bafe of Ifofceles Triangles ...
Página 15
... Angles . But the Angles 13 of this . ABC , ABD , together , are alfo equal to two Right Angles . Now taking away the common Angle ABC , and the remaining Angle ABE is equal to the re- maining Angle ABD , the lefs to the greater , which ...
... Angles . But the Angles 13 of this . ABC , ABD , together , are alfo equal to two Right Angles . Now taking away the common Angle ABC , and the remaining Angle ABE is equal to the re- maining Angle ABD , the lefs to the greater , which ...
Página 16
... Angles CEA , AED , are equal to the Angles AED , DEB . Take away the Common 4x.3 . Angle AED , and the Angle remaining CEA , is † equal to the Angle remaining BED . For the fame Reafon , the Angle CEB fhall be equal to the Angle DEA ...
... Angles CEA , AED , are equal to the Angles AED , DEB . Take away the Common 4x.3 . Angle AED , and the Angle remaining CEA , is † equal to the Angle remaining BED . For the fame Reafon , the Angle CEB fhall be equal to the Angle DEA ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Página 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...
Página 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.
Página 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Página 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...
Página 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.
Página 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.
Página 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.