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
... Proportion different from Euclid's ; and which com- prehends but one of the two Species of Proportion , taking in only commenfurable Quantities . Which great Fault no Logi- cian or Geometrician would have ever pardoned , had not thofe ...
... Proportion different from Euclid's ; and which com- prehends but one of the two Species of Proportion , taking in only commenfurable Quantities . Which great Fault no Logi- cian or Geometrician would have ever pardoned , had not thofe ...
Página 117
... Proportion to each other , which being multiplied can exceed one another , V. Magnitudes are faid to be in the fame Ratio , the first to the fecond , and the third to the fourth , when the Equimultiples of the first and third , compared ...
... Proportion to each other , which being multiplied can exceed one another , V. Magnitudes are faid to be in the fame Ratio , the first to the fecond , and the third to the fourth , when the Equimultiples of the first and third , compared ...
Página 118
... Proportion , are called Proportionals . Expounders ufually lay down here that Definition which Euclid has given for Numbers only , in his se- venth Book , viz . That Magnitudes are faid to be Proportionals , when the firft is the fame ...
... Proportion , are called Proportionals . Expounders ufually lay down here that Definition which Euclid has given for Numbers only , in his se- venth Book , viz . That Magnitudes are faid to be Proportionals , when the firft is the fame ...
Página 120
... Proportion than the Third to the Fourth , VIII . Analogy is a Similitude of Proportions , IX . Analogy at least confifts of three Terms . X. When three Magnitudes are Proportionals , the First is faid to have to the Third , a Duplicate ...
... Proportion than the Third to the Fourth , VIII . Analogy is a Similitude of Proportions , IX . Analogy at least confifts of three Terms . X. When three Magnitudes are Proportionals , the First is faid to have to the Third , a Duplicate ...
Página 121
... Proportion , is when , as the Antece- dent is to the Confequent , fo is the Antecedent to the Confequent ; and as the Confequent is to any other , fo is the Confequent to any other . XX . Perturbate Proportion , is when there are three ...
... Proportion , is when , as the Antece- dent is to the Confequent , fo is the Antecedent to the Confequent ; and as the Confequent is to any other , fo is the Confequent to any other . XX . Perturbate Proportion , is when there are three ...
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.