The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 Seiten |
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Seite 16
... shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a ...
... shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a ...
Seite 28
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore , the greater angle , & c . Q. E. D. See N. a 3. 1 . PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a ...
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore , the greater angle , & c . Q. E. D. See N. a 3. 1 . PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a ...
Seite 29
... shown that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . B C Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the ...
... shown that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . B C Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle BDC of the ...
Seite 32
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . IF two triangles have two angles of one equal to two angles of the other ...
... shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. PROP . XXVI . THEOR . IF two triangles have two angles of one equal to two angles of the other ...
Seite 36
... shown that the angle AGK is equal to the angle GHF ; there- fore also AGK is equal to GKD ; and they are alternate angles ; E. b 27.1 . therefore AB is parallel b to CD . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB ...
... shown that the angle AGK is equal to the angle GHF ; there- fore also AGK is equal to GKD ; and they are alternate angles ; E. b 27.1 . therefore AB is parallel b to CD . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB ...
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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2015 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2022 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Beliebte Passagen
Seite 30 - Any two sides of a triangle are together greater than the third side.
Seite 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Seite 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 165 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Seite 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Seite 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografische Informationen
| Titel | The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
| Autor/in | Robert Simson |
| Verlag | Mathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 518 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |