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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Ergebnisse 6-10 von 94
Seite 166
See N IN a right angled triangle , if a perpendicular be drawn from the right angle to the base , the triangles on each side of it are similar to the whole triangle , and to one another . a 32. 1 Let ABC be a right angled triangle ...
See N IN a right angled triangle , if a perpendicular be drawn from the right angle to the base , the triangles on each side of it are similar to the whole triangle , and to one another . a 32. 1 Let ABC be a right angled triangle ...
Seite 174
See N. UPON a given straight line to describe a rectili . neal figure similar , and similarly situated to a given rectilineal figure , aLet AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is ...
See N. UPON a given straight line to describe a rectili . neal figure similar , and similarly situated to a given rectilineal figure , aLet AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is ...
Seite 175
1 the rectilineal figures ABHG , CDEF are equiangular , and have Book VI . their sides about the equal angles proportionals , they are similar e 1. def.6 . to one another e , Next , Let it be required to describe upon a given straight ...
1 the rectilineal figures ABHG , CDEF are equiangular , and have Book VI . their sides about the equal angles proportionals , they are similar e 1. def.6 . to one another e , Next , Let it be required to describe upon a given straight ...
Seite 176
Therefore , similar triangles , & c . Q. E. D. Cor . From this it is manifest , that if three straight lines be proportionals , as the first is to the third , so is any triangle upon the first to a similar , and similarly described ...
Therefore , similar triangles , & c . Q. E. D. Cor . From this it is manifest , that if three straight lines be proportionals , as the first is to the third , so is any triangle upon the first to a similar , and similarly described ...
Seite 177
similar to the polygon FGHKL , the angle BAE is equal to the Book VI . angle GFL 2 , and BA is to AE as GF to FL a ; wherefore , be cause the triangles ABE , FGL have an angle in one equal to a 1.def.6 . an angle in the other ...
similar to the polygon FGHKL , the angle BAE is equal to the Book VI . angle GFL 2 , and BA is to AE as GF to FL a ; wherefore , be cause the triangles ABE , FGL have an angle in one equal to a 1.def.6 . an angle in the other ...
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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2018 |
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
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 |