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 65
Similar Segments of Circles are tbose , which include equal Angles , or whereof the Angles in them are equal PROPOSITION I. PROBLEM To find the Centre of a Circle given . ET A B C be the Circle given . It is required to find the Centre ...
Similar Segments of Circles are tbose , which include equal Angles , or whereof the Angles in them are equal PROPOSITION I. PROBLEM To find the Centre of a Circle given . ET A B C be the Circle given . It is required to find the Centre ...
Seite 86
FOR if this be possible , let the two similar and unequal Segments ACB , ADB , of two Circles , stand upon the Right Line A B on the fame Side thereof . Draw A CD , and let CB , BD , be joined . Now , because the Segment ACB is similar ...
FOR if this be possible , let the two similar and unequal Segments ACB , ADB , of two Circles , stand upon the Right Line A B on the fame Side thereof . Draw A CD , and let CB , BD , be joined . Now , because the Segment ACB is similar ...
Seite 87
Therefore , similar Segments of Circles , being upon equal Right Lines , are equal to one another ; which was to be demonstrated . PROPOSITION XXV . PROBLEM . A Segment of a Circle being given , to describe the Circle whereof it is the ...
Therefore , similar Segments of Circles , being upon equal Right Lines , are equal to one another ; which was to be demonstrated . PROPOSITION XXV . PROBLEM . A Segment of a Circle being given , to describe the Circle whereof it is the ...
Seite 88
But those similar Segments of Circles , that are 1 24 of rbis . upon equal Right Lines , are I equal to each other . Def . 11. Therefore the Segment BAC will be + equal to 4. I , DELFD . Therefore the remaining Circumference BKC shall ...
But those similar Segments of Circles , that are 1 24 of rbis . upon equal Right Lines , are I equal to each other . Def . 11. Therefore the Segment BAC will be + equal to 4. I , DELFD . Therefore the remaining Circumference BKC shall ...
Seite 159
If a Perpendicular be drawn , in a Right angled Triangle , from ibe Right Angle to the Base , tben ibe Triangle on each side of the Perpen , dicular are similar , borb to the Wbole , and also to one another .
If a Perpendicular be drawn , in a Right angled Triangle , from ibe Right Angle to the Base , tben ibe Triangle on each side of the Perpen , dicular are similar , borb to the Wbole , and also to one another .
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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
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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 |