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 sider |
Inni boken
Side 28
See N. ANY two sides of a triangle are together greater than the third side . A Let
ABC be a triangle ; any two sides of it together are greater than the third side , viz
. the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and ...
See N. ANY two sides of a triangle are together greater than the third side . A Let
ABC be a triangle ; any two sides of it together are greater than the third side , viz
. the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and ...
Side 31
Let ABC , DEF be two triangles which have the two sides Book I. AB , AC equal to
the two DE , DF , each to each , viz . ... Of the two sides DE , DF , let DE be the
side which is not greater than the other , and at the point D , in the straight line DE
...
Let ABC , DEF be two triangles which have the two sides Book I. AB , AC equal to
the two DE , DF , each to each , viz . ... Of the two sides DE , DF , let DE be the
side which is not greater than the other , and at the point D , in the straight line DE
...
Side 201
1 . and because AD is equal to BC , and AF to FB , the two sides FA , AD are
equal to the two FB , BC , each to each ; and the base DF was F proved equal to
the base FC ; therefore the angle FAD is equal d to the angle d 8.1 . FBC : again ,
it ...
1 . and because AD is equal to BC , and AF to FB , the two sides FA , AD are
equal to the two FB , BC , each to each ; and the base DF was F proved equal to
the base FC ; therefore the angle FAD is equal d to the angle d 8.1 . FBC : again ,
it ...
Side 217
4 . either be within the triangle , or in one of its sides , or without it . First , let the
centre X be within the triangle , and join LX , MX , NX : AB is greater than LX : if
not , AB must either be equal to , or less than LX ; first , let it be equal : then
because ...
4 . either be within the triangle , or in one of its sides , or without it . First , let the
centre X be within the triangle , and join LX , MX , NX : AB is greater than LX : if
not , AB must either be equal to , or less than LX ; first , let it be equal : then
because ...
Side 233
as and so as that the sides CL , LB be in a straight line ; therefore Book XI . the
straight line LM , which is at right angles to the plane in which the bases are , in
the point L , is common a to the two so- a 13. 11 . lids AE , CF : let the other
insisting ...
as and so as that the sides CL , LB be in a straight line ; therefore Book XI . the
straight line LM , which is at right angles to the plane in which the bases are , in
the point L , is common a to the two so- a 13. 11 . lids AE , CF : let the other
insisting ...
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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
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 Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 30 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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.
Side 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.
Side 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.
Side 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.
Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | 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 |
| Forfatter | Robert Simson |
| Utgiver | 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 fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 518 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |