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 |
Inni boken
Resultat 1-5 av 13
Side 16
DB and the straight line AB is divided into two equal parts in the point D. Which
was to be done . D B PROP . XI . PROB . To draw a straight line at right angles to
a given straight line , from a given point in the same . Let AB be a given straight ...
DB and the straight line AB is divided into two equal parts in the point D. Which
was to be done . D B PROP . XI . PROB . To draw a straight line at right angles to
a given straight line , from a given point in the same . Let AB be a given straight ...
Side 36
Then , because the straight line HF falls upon the parallels AH , EF , the angles
AHF , HFE are together equal ( 29. 1. ) ... To describe a parallelogram equal to a
given retilineal figure , and having an angle equal to a given rectilineal angle .
Then , because the straight line HF falls upon the parallels AH , EF , the angles
AHF , HFE are together equal ( 29. 1. ) ... To describe a parallelogram equal to a
given retilineal figure , and having an angle equal to a given rectilineal angle .
Side 89
1 Let ABCDE be the given equilateral and equiangular pentagon : it is required to
inscribe a circle in the pentagon ABCDE . Bisect ( 9. 1. ) the angles BCD , CDE by
the straight lines CF , DF , and from the point F , in which they meet , draw the ...
1 Let ABCDE be the given equilateral and equiangular pentagon : it is required to
inscribe a circle in the pentagon ABCDE . Bisect ( 9. 1. ) the angles BCD , CDE by
the straight lines CF , DF , and from the point F , in which they meet , draw the ...
Side 181
... each , and situated in the same order , the solid angles are equal ( B. 11. )
each to each . Therefore the solid AL is similar ( 11. def . 11. ) to the solid CD .
Wherefore from a given straight line AB , a solid parallelopiped AL has been
described ...
... each , and situated in the same order , the solid angles are equal ( B. 11. )
each to each . Therefore the solid AL is similar ( 11. def . 11. ) to the solid CD .
Wherefore from a given straight line AB , a solid parallelopiped AL has been
described ...
Side 249
... it is demonstrated indirectly , that the circle touches a straight line : whereas in
the 17th , 33d , and 37th propositions of ... where mention is made of a given
angle , though there neither is , nor can be any thing in the proposition relating to
a ...
... it is demonstrated indirectly , that the circle touches a straight line : whereas in
the 17th , 33d , and 37th propositions of ... where mention is made of a given
angle , though there neither is , nor can be any thing in the proposition relating to
a ...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |
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 |