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 |
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Side 483
The sine , versed sine , tangent , and seCant , of any arch which is the measure
of any given angle ABC , is to the sine , versed sine , tangent , and secant , of any
other arch which is the measure of the same angle , as the rachius of the first is ...
The sine , versed sine , tangent , and seCant , of any arch which is the measure
of any given angle ABC , is to the sine , versed sine , tangent , and secant , of any
other arch which is the measure of the same angle , as the rachius of the first is ...
Side 504
And since by this proposition the co - sine of the hypothenuse BC is to the radius
as the co - tangent of the angle ABC to the tangent of the angle ACB . But as the
radius is to the co - tangent of the angle ACB , so is the tangent of the same to the
...
And since by this proposition the co - sine of the hypothenuse BC is to the radius
as the co - tangent of the angle ABC to the tangent of the angle ACB . But as the
radius is to the co - tangent of the angle ACB , so is the tangent of the same to the
...
Side 510
18. the sine of the hypothenuse BC is to the radius ( or the sine of the right angle
at A ) as the sine of the side AC to the sine of the angle B. And in like manner , the
sine of BC is to the sine of the angle A , as the sine of AB 10 the sine of the ...
18. the sine of the hypothenuse BC is to the radius ( or the sine of the right angle
at A ) as the sine of the side AC to the sine of the angle B. And in like manner , the
sine of BC is to the sine of the angle A , as the sine of AB 10 the sine of the ...
Side 511
22. the co - sine of the angle B is to the sine of the angle BCA as ( the co - sine of
the side AC is to the radius ; that is , by prop . 22. as ) the co - sine of the angle D
to the sine of the angle DCA ; and , by permutation , the co - sine of the angle B ...
22. the co - sine of the angle B is to the sine of the angle BCA as ( the co - sine of
the side AC is to the radius ; that is , by prop . 22. as ) the co - sine of the angle D
to the sine of the angle DCA ; and , by permutation , the co - sine of the angle B ...
Side 513
... let the side BC be greater than BA , and let BH be made equal to BC ; AH will
therefore be the excess of the sides BC , BA ; let HK be drawn perpendicular to
AD , and since AG is the versed sine of the base AC , and AK the versed sine of
the ...
... let the side BC be greater than BA , and let BH be made equal to BC ; AH will
therefore be the excess of the sides BC , BA ; let HK be drawn perpendicular to
AD , and since AG is the versed sine of the base AC , and AK the versed sine of
the ...
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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |
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 |