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 |
Dentro del libro
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Página 117
... Ratio , is a certain mutual Habitude of the Magni- tudes of the Jame kind , according to Quantity . IV . Magnitudes are faid to have Proportion to each other , which being multiplied can exceed one another , V. Magnitudes are faid to be ...
... Ratio , is a certain mutual Habitude of the Magni- tudes of the Jame kind , according to Quantity . IV . Magnitudes are faid to have Proportion to each other , which being multiplied can exceed one another , V. Magnitudes are faid to be ...
Página 118
... Ratio , the first to the second , as the third to the fourth . VI . Magnitudes that have the fame Proportion , are ... Ratio , according to the Conditions that Magnitudes in the fame Ratio must have , laid down ' in the fifth Definition ...
... Ratio , the first to the second , as the third to the fourth . VI . Magnitudes that have the fame Proportion , are ... Ratio , according to the Conditions that Magnitudes in the fame Ratio must have , laid down ' in the fifth Definition ...
Página 120
... Ratio to what it has to the Second . XI . But when four Magnitudes are Proportionals , the First shall have a Trilicate Ratio to the Fourth of what it has to the Second ; and fo always one more in Order , as the Proportionals fhall be ...
... Ratio to what it has to the Second . XI . But when four Magnitudes are Proportionals , the First shall have a Trilicate Ratio to the Fourth of what it has to the Second ; and fo always one more in Order , as the Proportionals fhall be ...
Página 130
... Ratio to D , than C has to D. I fay , moreover , that D has a greater Ratio to C , than it has to AB ; for the fame Conftruction remaining , we demonftrate , as be- fore , that N exceeds K , but not FH . And N is a Multiple of D , and ...
... Ratio to D , than C has to D. I fay , moreover , that D has a greater Ratio to C , than it has to AB ; for the fame Conftruction remaining , we demonftrate , as be- fore , that N exceeds K , but not FH . And N is a Multiple of D , and ...
Página 140
... Ratio . The Demonftration of Converse Ratio , laid down in this Corollary , is only particular , For Alternation ( which is ufed herein ) cannot be apply'd but when the four proportional Magnitudes are all of the fame Kind , as will ...
... Ratio . The Demonftration of Converse Ratio , laid down in this Corollary , is only particular , For Alternation ( which is ufed herein ) cannot be apply'd but when the four proportional Magnitudes are all of the fame Kind , as will ...
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.