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 sider |
Inni boken
Resultat 1-5 av 72
Side
... shall know whether we are to take the Sum or the Difference of the Vertical Angles or Bases , for the fought Angle or Bafe : And in the Calculation of that Angle have left us in the dark as to its Species ; as appears by my Obfervations ...
... shall know whether we are to take the Sum or the Difference of the Vertical Angles or Bases , for the fought Angle or Bafe : And in the Calculation of that Angle have left us in the dark as to its Species ; as appears by my Obfervations ...
Side 21
... shall GK be alfo equal to C ; but FG is likewife equal to B ; and confequently the three Right Lines KF , FG , KG , are equal to the three Right Lines A , B , C ; where- fore the Triangle K F G is made of three Right Lines KF , FG , GK ...
... shall GK be alfo equal to C ; but FG is likewife equal to B ; and confequently the three Right Lines KF , FG , KG , are equal to the three Right Lines A , B , C ; where- fore the Triangle K F G is made of three Right Lines KF , FG , GK ...
Side 23
... shall also have the Angles , contain'd under the equal Sides , the one greater than the other . LE ET there be two Triangles ABC , DEF , having two Sides A B , A C , each equal to two Sides DE , DF , viz . the Side AB equal to the Side ...
... shall also have the Angles , contain'd under the equal Sides , the one greater than the other . LE ET there be two Triangles ABC , DEF , having two Sides A B , A C , each equal to two Sides DE , DF , viz . the Side AB equal to the Side ...
Side 26
... shall be parallel . LET the Right Line EF , falling upon two Right Lines AB , CD , make the alternate Angels AEF , EFD , equal between themselves . I fay the Right Line AB is parallel to CD . For if it be not parallel , AB and CD ...
... shall be parallel . LET the Right Line EF , falling upon two Right Lines AB , CD , make the alternate Angels AEF , EFD , equal between themselves . I fay the Right Line AB is parallel to CD . For if it be not parallel , AB and CD ...
Side 27
... , or the inward Angles on the fame Side together equal to two Right Angles , the two Right Lines Shall be parallel between themselves ; which was to be demonitrated . PRO- * 13 of this . † 4x . 12 . Book I. Euclid's ELEMENTS . 27.
... , or the inward Angles on the fame Side together equal to two Right Angles , the two Right Lines Shall be parallel between themselves ; which was to be demonitrated . PRO- * 13 of this . † 4x . 12 . Book I. Euclid's ELEMENTS . 27.
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Side 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...
Side 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.
Side 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Side 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...
Side 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.
Side 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.
Side 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.