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 ... |
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Page 340
... preffes the Length of the Subtangent AT . Fig.4 . After Neper's Death , the excellent Mr.Henry Briggs , by great Pains , made and published Tables of Loga- rithms according to this Form . Now fince in thefe rithms 340 Of LOGARITHMS .
... preffes the Length of the Subtangent AT . Fig.4 . After Neper's Death , the excellent Mr.Henry Briggs , by great Pains , made and published Tables of Loga- rithms according to this Form . Now fince in thefe rithms 340 Of LOGARITHMS .
Page 356
... Subtangent , will every where be a conftant and given Length . And this is one of the chief Proper- ties of the ... Subtan- gents as gents of their Curves . For let HBD , 356 Of LOGARITHMS .
... Subtangent , will every where be a conftant and given Length . And this is one of the chief Proper- ties of the ... Subtan- gents as gents of their Curves . For let HBD , 356 Of LOGARITHMS .
Page 357
... Subtangent AT is to the Subtangent M X. For let there be fuppofed an infinite Number of mean proportional Terms between AB , CD , or NM , QY , in the Ratio of AB to ab , or MN to mn ; and fince ABMN , then will ab = mn , alfo be no ...
... Subtangent AT is to the Subtangent M X. For let there be fuppofed an infinite Number of mean proportional Terms between AB , CD , or NM , QY , in the Ratio of AB to ab , or MN to mn ; and fince ABMN , then will ab = mn , alfo be no ...
Page 358
... Subtangent thereof MX fhall be conftant and invariable , and the small Triangle Non fhall be fimilar to the Triangle XMN . But it has been prov'd , that the Increment no = Mm Xa Noxa ; and fono : No :: Noxa : No :: a : 1. But as no is ...
... Subtangent thereof MX fhall be conftant and invariable , and the small Triangle Non fhall be fimilar to the Triangle XMN . But it has been prov'd , that the Increment no = Mm Xa Noxa ; and fono : No :: Noxa : No :: a : 1. But as no is ...
Page 359
... Subtangent of the Lo- garithmical Curve expreffing Brigg's Logarithms ) fo is one Year or Unity to a Briggian Logarithm , answering to the Number Q Y. This Logarithm will be found o . 0217147 , and the Number answering to the fame is ...
... Subtangent of the Lo- garithmical Curve expreffing Brigg's Logarithms ) fo is one Year or Unity to a Briggian Logarithm , answering to the Number Q Y. This Logarithm will be found o . 0217147 , and the Number answering to the fame is ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Page 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...
Page 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.
Page 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Page 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...
Page 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.
Page 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.
Page 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.