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 79
Side 3
... Parallels are fuch Right Lines in the fame Plane , which if infinitely produc'd both Ways , would never meet . I. G POSTULATE S. RANT that a Right - Line may be drawn from any one Point to another . II . That a finite Right Line may be ...
... Parallels are fuch Right Lines in the fame Plane , which if infinitely produc'd both Ways , would never meet . I. G POSTULATE S. RANT that a Right - Line may be drawn from any one Point to another . II . That a finite Right Line may be ...
Side 26
... parallel to CD . For if it be not parallel , AB and CD , produc'd to- wards B and D , or towards A and C , will meet : Now let them be produc'd towards B and D , and meet in the Point G. * Then the outward Angle AEF of the Triangle * 16 ...
... parallel to CD . For if it be not parallel , AB and CD , produc'd to- wards B and D , or towards A and C , will meet : Now let them be produc'd towards B and D , and meet in the Point G. * Then the outward Angle AEF of the Triangle * 16 ...
Side 27
... parallel between themselves . LE ET the Right Line EF falling upon two Right Lines AB , CD , make the outward Angle EGB equal to the inward and oppofite Angle GHD ; or the inward Angles BGH , GHD on the fame Side together equal to two ...
... parallel between themselves . LE ET the Right Line EF falling upon two Right Lines AB , CD , make the outward Angle EGB equal to the inward and oppofite Angle GHD ; or the inward Angles BGH , GHD on the fame Side together equal to two ...
Side 28
... parallel Right Lines AB , CD . I fay the alternate An- gles , AGH , GHD , are equal between themselves ; the outward Angle , ÉGB , is equal to the inward one GHD , on the fame Side ; and the two inward ones , BGH , GHD , on the fame ...
... parallel Right Lines AB , CD . I fay the alternate An- gles , AGH , GHD , are equal between themselves ; the outward Angle , ÉGB , is equal to the inward one GHD , on the fame Side ; and the two inward ones , BGH , GHD , on the fame ...
Side 29
... parallel to one and the fame Right Line , are alfo parallel between themselves . LET AB and CD be Right Lines , each of which is parallel to the Right Line EF . I fay AB is alfo parallel to CD . For let the Right Line GK fall upon them ...
... parallel to one and the fame Right Line , are alfo parallel between themselves . LET AB and CD be Right Lines , each of which is parallel to the Right Line EF . I fay AB is alfo parallel to CD . For let the Right Line GK fall upon them ...
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.