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 |
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Side 387
given angle , will each contain a given number of these parts ; and , by
trigonometrical tables , the length of the sine , versed sine , tangent , and secant ,
of any angle , may be found in parts of which the radius contains a given number
; and ...
given angle , will each contain a given number of these parts ; and , by
trigonometrical tables , the length of the sine , versed sine , tangent , and secant ,
of any angle , may be found in parts of which the radius contains a given number
; and ...
Side 389
In any plane triangle BAC , whose two sides are BA , AC , and base BC , the less
of the two sides , which let be BA is to the greater AC , as the radius is to the
tangent of an angle ; and the radius is to the tangent of the excess of this angle ...
In any plane triangle BAC , whose two sides are BA , AC , and base BC , the less
of the two sides , which let be BA is to the greater AC , as the radius is to the
tangent of an angle ; and the radius is to the tangent of the excess of this angle ...
Side 403
therefore AF is the tangent of the arch AC ; and in the rectilineal triangle AEF ,
having a right angle at A , AE will be to the radius as AF to the tangent of the
angle AEF ( 1. Pl . Tr . ) ; but AE is the sine of the arch AB , and AF the tangent of
the ...
therefore AF is the tangent of the arch AC ; and in the rectilineal triangle AEF ,
having a right angle at A , AE will be to the radius as AF to the tangent of the
angle AEF ( 1. Pl . Tr . ) ; but AE is the sine of the arch AB , and AF the tangent of
the ...
Side 404
Let ABC be a spherical triangle , having a right angle at A ; the co - sine of the
hypothenuse BC will be to the radius , as the co - tangent of the angle ABC to the
tangent of the angle ACB . Describe the circle DE , of which B is the pole , and let
it ...
Let ABC be a spherical triangle , having a right angle at A ; the co - sine of the
hypothenuse BC will be to the radius , as the co - tangent of the angle ABC to the
tangent of the angle ACB . Describe the circle DE , of which B is the pole , and let
it ...
Side 411
For , by 17 , the sine of BA is to the radius , as the tangent of AC to the tangent of
the angle B ; and by 17 , and inversion , the radius is to the sine of AD , as the
tangent of D to the tangent of AC : therefore , ex æquo perturbate , the sine of BA
is ...
For , by 17 , the sine of BA is to the radius , as the tangent of AC to the tangent of
the angle B ; and by 17 , and inversion , the radius is to the sine of AD , as the
tangent of D to the tangent of AC : therefore , ex æquo perturbate , the sine of BA
is ...
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The Elements of Euclid, Viz; The First Six Books: Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP 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
Populære avsnitt
Side 45 - Ir 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.
Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 20 - ANY two angles of a triangle are together less than two right angles.
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 |
| Forfattere | Euclid, Robert Simson |
| Redaktør | Robert Simson |
| Utgiver | Desilver, Thomas & Company, 1838 |
| Original fra | University of Michigan |
| Digitalisert | 20. sep 2007 |
| Lengde | 416 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |