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 10
... fame Side , and having the fame Ends which the firft Right Lines have . FOR , if it be poffible , let two Right Lines A D DB , equal to two others AC , CB , each to each , be conftituted at different Points C and D , towards the fame ...
... fame Side , and having the fame Ends which the firft Right Lines have . FOR , if it be poffible , let two Right Lines A D DB , equal to two others AC , CB , each to each , be conftituted at different Points C and D , towards the fame ...
Página 11
... fame Side , having the fame Ends . But this is 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 ...
... fame Side , having the fame Ends . But this is 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 ...
Página 20
... fame Manner we demonftrate , that the Sides AB , BC , together , are greater than the Side CA ; and the Sides BC , CA , together , are greater than the Side AB . Therefore two Sides of any Triangle , bowfoever taken , are together ...
... fame Manner we demonftrate , that the Sides AB , BC , together , are greater than the Side CA ; and the Sides BC , CA , together , are greater than the Side AB . Therefore two Sides of any Triangle , bowfoever taken , are together ...
Página 27
... fame Side , or the inward Angles on the fame Side together equal to two Right Angles , the two Right Lines fhall be parallel between themselves . LE ET the Right Line EF falling upon two Right Lines AB , CD , make the outward Angle EGB ...
... fame Side , or the inward Angles on the fame Side together equal to two Right Angles , the two Right Lines fhall be parallel between themselves . LE ET the Right Line EF falling upon two Right Lines AB , CD , make the outward Angle EGB ...
Página 28
... fame Side ; and the two inward ones , BGH , GHD , on the fame Side , are together equal to two Right Angles . For if AGH be unequal to GHD , one of them will be the greater . Let this be AGH ; then because the Angle AGH is greater than ...
... fame Side ; and the two inward ones , BGH , GHD , on the fame Side , are together equal to two Right Angles . For if AGH be unequal to GHD , one of them will be the greater . Let this be AGH ; then because the Angle AGH is greater than ...
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.