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 191
... Cylinder is that fixed Right Line about which the Parallelogram is turned . XXIII . And the Bafes of a Cylinder are the Circles that be defcribed by the Motion of the two oppofite Sides of the Parallelogram . XXIV . Similar Cones and ...
... Cylinder is that fixed Right Line about which the Parallelogram is turned . XXIII . And the Bafes of a Cylinder are the Circles that be defcribed by the Motion of the two oppofite Sides of the Parallelogram . XXIV . Similar Cones and ...
Página 254
... Cylinder , having the fame Bafe , and an equal Altitude . LET a Cone have the fame Bafe as a Cylinder , viz . the Circle ABCD , and an Altitude equal to it . I fay the Cone is a third Part of the Cylinder , that is , the Cylinder is ...
... Cylinder , having the fame Bafe , and an equal Altitude . LET a Cone have the fame Bafe as a Cylinder , viz . the Circle ABCD , and an Altitude equal to it . I fay the Cone is a third Part of the Cylinder , that is , the Cylinder is ...
Página 255
... Cylinder be not triple to the Cone , it fhall be greater or less than triple thereof . First let it be greater than ... Cylinder , and this Prifm will be greater than one half of the Cylinder ; because , if a Square be circumfcrib'd ...
... Cylinder be not triple to the Cone , it fhall be greater or less than triple thereof . First let it be greater than ... Cylinder , and this Prifm will be greater than one half of the Cylinder ; because , if a Square be circumfcrib'd ...
Página 256
... Cylinder ; and doing this continually , we shall at laft have certain Portions of the Cylinder left , that are lefs than the Excess by which the Cylinder exceeds triple the Cone . Now let thefe Portions remaining be A E , EB , BF , FC ...
... Cylinder ; and doing this continually , we shall at laft have certain Portions of the Cylinder left , that are lefs than the Excess by which the Cylinder exceeds triple the Cone . Now let thefe Portions remaining be A E , EB , BF , FC ...
Página 257
... Cylinder . Let thefe Segments be thofe that are on AE , EB , BF , FC , CG , GD , DH , HA , and then the remaining ... Cylinder ; but the Pyramid whose Base is the Polygon AEBFCGDH , and Ver- tex the fame as that of the Cone , is one ...
... Cylinder . Let thefe Segments be thofe that are on AE , EB , BF , FC , CG , GD , DH , HA , and then the remaining ... Cylinder ; but the Pyramid whose Base is the Polygon AEBFCGDH , and Ver- tex the fame as that of the Cone , is one ...
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.