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 Work |
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Seite 118
Ratio is a certain mutual Habitude of Magnitudes of the same Kind , according to Quantity . IV . Magnitudes are said to bave Proportion to each other , which , being multiplied , can exceed one another . V. Magnitudes are said to be in ...
Ratio is a certain mutual Habitude of Magnitudes of the same Kind , according to Quantity . IV . Magnitudes are said to bave Proportion to each other , which , being multiplied , can exceed one another . V. Magnitudes are said to be in ...
Seite 119
... and also that of the third less than that of the fourth , and these Things happen according to every Multiplication whatsoever : Then the four Magnitudes are in the same Ratio ; the first to the fecond , as the third to the fourth .
... and also that of the third less than that of the fourth , and these Things happen according to every Multiplication whatsoever : Then the four Magnitudes are in the same Ratio ; the first to the fecond , as the third to the fourth .
Seite 121
X. When three Magnitudes are Proportionals , the first is said to have , to the third , a duplicate Ratio to what it has to the second . XI . But when four Magnitudes are continued Proportionals , ibe first hall have a triplicate Ratio ...
X. When three Magnitudes are Proportionals , the first is said to have , to the third , a duplicate Ratio to what it has to the second . XI . But when four Magnitudes are continued Proportionals , ibe first hall have a triplicate Ratio ...
Seite 131
1 . to D , than C has to D. I say , moreover , that D has à greater Ratio to C than it has to AB : For the fame Construction remaining , we demonstrate , as before , that N exceeds K , but not FH . And N is a Multiple of D , and FH and ...
1 . to D , than C has to D. I say , moreover , that D has à greater Ratio to C than it has to AB : For the fame Construction remaining , we demonstrate , as before , that N exceeds K , but not FH . And N is a Multiple of D , and FH and ...
Seite 141
The Demonstration of converse Ratio , laid down in this Corollary , is only particular . For Alternatian ( which is used herein ) cannot be applied but when the four proportionat Magnitudes are all of the same Kind ...
The Demonstration of converse Ratio , laid down in this Corollary , is only particular . For Alternatian ( which is used herein ) cannot be applied but when the four proportionat Magnitudes are all of the same Kind ...
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Euclid's Elements of Geometry, from the Latin Translation of Commandine: To ... John Keill Keine Leseprobe verfügbar - 2017 |
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added alſo Altitude Baſe becauſe Centre Circle Circle ABCD Circumference common Cone conſequently contained Cylinder demonſtrated deſcribed Diameter Difference Diſtance divided double draw drawn equal equal Angles equiangular Equimultiples exceeds fall fame firſt fore four fourth given greater half join leſs likewiſe Logarithm Magnitudes manner mean Multiple Number oppoſite parallel Parallelogram perpendicular Place Plane Point Polygon Priſms produced Prop Proportion PROPOSITION proved Pyramid Ratio Reaſon Rectangle remaining Right Angles Right Line Right Line A B Right-lined Figure ſaid ſame ſay ſecond Segment Series ſhall ſhall be equal Sides ſimilar ſince Sine Solid ſome Sphere Square taken Terms THEOREM thereof theſe third thoſe thro touch Triangle Triangle A B C Unity Whence Wherefore whole whoſe Baſe
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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 22 - ... 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...
Bibliografische Informationen
| Titel | 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 Work |
| Autor/in | John Keill |
| Ausgabe | 11 |
| Verlag | W. Strahan, 1772 |
| Original von | University of Michigan |
| Digitalisiert | 8. Juni 2007 |
| Länge | 399 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |