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 8
... and join FC , GB . Then , because AF is equal to AG , and A B to AC , the two Right Lines FA , AC , are equal to the two Lines GA , A B , each to each , and contain the com+ 4 of this . mon Angle FAG ; therefore the Base F C is ...
... and join FC , GB . Then , because AF is equal to AG , and A B to AC , the two Right Lines FA , AC , are equal to the two Lines GA , A B , each to each , and contain the com+ 4 of this . mon Angle FAG ; therefore the Base F C is ...
Seite 9
I say , the Side A B is likewise equal to the Side A C. For if A B be not equal to AC , let one of them , as AB , be the greater , from which cut off B D equal to AC + , and join DC . Then , because B D is equal to 3 of this .
I say , the Side A B is likewise equal to the Side A C. For if A B be not equal to AC , let one of them , as AB , be the greater , from which cut off B D equal to AC + , and join DC . Then , because B D is equal to 3 of this .
Seite 10
Suppose D fell without the Triangle A BC ; join Ċ Ď . Then , because AC is equal to AD , the Angle + softbis . ACD will be equal + to the Angle A DC , and confequently the Angle ADC is greater than the Angle BCD ; wherefore the Angle ...
Suppose D fell without the Triangle A BC ; join Ċ Ď . Then , because AC is equal to AD , the Angle + softbis . ACD will be equal + to the Angle A DC , and confequently the Angle ADC is greater than the Angle BCD ; wherefore the Angle ...
Seite 12
Aflume any Point D in the Right Line A B , and + 3 of this , cut off A E from the Line AC equal to A D + ; join | 1 of tbis . D E , and thereon make the equilateral Triangle DE F , and join AF . I say , the Angle B A C is cut into two ...
Aflume any Point D in the Right Line A B , and + 3 of this , cut off A E from the Line AC equal to A D + ; join | 1 of tbis . D E , and thereon make the equilateral Triangle DE F , and join AF . I say , the Angle B A C is cut into two ...
Seite 13
Triangle F D E , and join FC . I say , the Rights of this . Line F C is drawn from the Point C , given in the Right Line A B , at Right Angles to A B. For , because DC is equal to C E , and F C is common , the two Lines DC , CF , are ...
Triangle F D E , and join FC . I say , the Rights of this . Line F C is drawn from the Point C , given in the Right Line A B , at Right Angles to A B. For , because DC is equal to C E , and F C is common , the two Lines DC , CF , are ...
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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 |