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 Plane and Spherical Trigonometry; with a Preface, Shewing the Usefulness and Excellency of this WorkW. Strahan, 1772 - 399 Seiten |
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Seite 118
... Ratio is a certain mutual Habitude of Mag- nitudes of the fame Kind , according to Quan- tity . 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 Mag- nitudes of the fame Kind , according to Quan- tity . IV . Magnitudes are faid to have Proportion to each other , which , being multiplied , can exceed one another . V. Magnitudes are faid to be ...
Seite 119
... Ratio , according to the Conditions that Magnitudes in the fame Ratio must have according to the fifth Definition ; and let the firft be a Multiple of the fecond : I fay , the third is alfo the fame Mul- tiple of the fourth . For ...
... Ratio , according to the Conditions that Magnitudes in the fame Ratio must have according to the fifth Definition ; and let the firft be a Multiple of the fecond : I fay , the third is alfo the fame Mul- tiple of the fourth . For ...
Seite 121
... Ratio to what it has to the fecond . XI . But when four Magnitudes are continued Proportionals , the first shall have a triplicate Ratio to the fourth of what it has to the fe- cond ; and fo always one more in Order , as the ...
... Ratio to what it has to the fecond . XI . But when four Magnitudes are continued Proportionals , the first shall have a triplicate Ratio to the fourth of what it has to the fe- cond ; and fo always one more in Order , as the ...
Seite 131
... Ratio † Def . 7 . 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 ...
... Ratio † Def . 7 . 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 ...
Seite 141
... Ratio . The Demonftration of converfe Ratio , laid down in this Corollary , is only particular . For Alternation ( which is ufed herein ) cannot be applied but when the four proportional Magnitudes are all of the fame Kind , as will ...
... Ratio . The Demonftration of converfe Ratio , laid down in this Corollary , is only particular . For Alternation ( which is ufed herein ) cannot be applied but when the four proportional Magnitudes are all of the fame Kind , as will ...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2018 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2017 |
Euclid's Elements of Geometry: From the Latin Translation of Commandine. to ... John Keill Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
A B C adjacent Angles alfo equal alſo Angle ABC Baſe becauſe bifected Centre Circle ABCD Circumference Cofine Cone confequently Coroll Cylinder defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reaſon fecond fhall be equal fimilar fince firft folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Polygon Prifm Prop PROPOSITION Pyramid Quadrant Ratio Reafon Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure Segment ſhall Sides A B Sine Square Subtangent thefe THEOREM thofe thoſe tiple Triangle ABC Unity Vertex the Point Wherefore whofe Bafe whoſe
Beliebte Passagen
Seite 195 - 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.
Seite 165 - 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.
Seite 169 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles...
Seite xxii - ... sides equal to them of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB...
Seite 54 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 123 - GB is equal to E, and HD to F; GB and HD together are equal to E and F together : wherefore as many magnitudes as...
Seite 215 - 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...
Seite 196 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.
Seite 161 - And because HE is parallel to KC, one of the sides of the triangle DKC, as CE to ED, so is...
Seite 207 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. V. The inclination of a straight line to a plane...