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 102
To apply a Right Line in a given Circle , equal to a given Right Line , whose Lengib . does not exceed the Diameter of the Circle . ET the Circle given be A BC , and the given Right Line , not greater than the Diameter , be D. It is ...
To apply a Right Line in a given Circle , equal to a given Right Line , whose Lengib . does not exceed the Diameter of the Circle . ET the Circle given be A BC , and the given Right Line , not greater than the Diameter , be D. It is ...
Seite 118
Magnitudes are said to bave Proportion to each other , which , being multiplied , can exceed one another . V. Magnitudes are said to be in the same Ratio , the first to the second , and the third to the fourib ; when the Equimultiples ...
Magnitudes are said to bave Proportion to each other , which , being multiplied , can exceed one another . V. Magnitudes are said to be in the same Ratio , the first to the second , and the third to the fourib ; when the Equimultiples ...
Seite 121
Wben , of Equimultiples , the Multiple of the firft exceeds the Multiple of the second , but the Multiple of the third does not exceed the Mul . tiple of the fourth ; then the first to the second is said to have a greater Proportion ...
Wben , of Equimultiples , the Multiple of the firft exceeds the Multiple of the second , but the Multiple of the third does not exceed the Mul . tiple of the fourth ; then the first to the second is said to have a greater Proportion ...
Seite 126
5. of M , then + L will exceed N ; if K ibis multiples of the first and third have the same Proportion. be equal to M , L will be equal to N ; and if K is less than M , then L will be less than N : But K and L are Equimultiples of E and ...
5. of M , then + L will exceed N ; if K ibis multiples of the first and third have the same Proportion. be equal to M , L will be equal to N ; and if K is less than M , then L will be less than N : But K and L are Equimultiples of E and ...
Seite 127
Because it is demonstrated , if K exceeds M , then L will exceed N ; and if K be equal to M , L will be equal to N ; and if K be less than M , L will be less than N : It is manifeft , likewise , if M exceeds K , that N fall exceed L ...
Because it is demonstrated , if K exceeds M , then L will exceed N ; and if K be equal to M , L will be equal to N ; and if K be less than M , L will be less than N : It is manifeft , likewise , if M exceeds K , that N fall exceed L ...
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Euclid's Elements of Geometry, from the Latin Translation of Commandine: To ... John Keill Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
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
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 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 |