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 214
EVERY cone is a third part of a cylinder which has the same base , and is of an
equal altitude with it . Let a cone have the same base with a cylinder , viz . the
circle ABCD , and the same altitude . The cone is the third part of the cylinder ;
that is ...
EVERY cone is a third part of a cylinder which has the same base , and is of an
equal altitude with it . Let a cone have the same base with a cylinder , viz . the
circle ABCD , and the same altitude . The cone is the third part of the cylinder ;
that is ...
Side 222
the cylinder to the cylinder ' ; for every cone is the third part of the cylinder upon
the same base , and of the same altitude : therefore also the cylinder has to the
cylinder the triplicate ratio of that which AC has to EG . Wherefore similar cones ...
the cylinder to the cylinder ' ; for every cone is the third part of the cylinder upon
the same base , and of the same altitude : therefore also the cylinder has to the
cylinder the triplicate ratio of that which AC has to EG . Wherefore similar cones ...
Side 223
02 z it is to be shown , that the cylinder AH is to the cylinder HC , as the axis EK to
the axis KF . Produce the axis EF both ways ; and take any number of straight
lines EN , NL , each equal to EK ; and any number FX , XM each equal to FK ;
and ...
02 z it is to be shown , that the cylinder AH is to the cylinder HC , as the axis EK to
the axis KF . Produce the axis EF both ways ; and take any number of straight
lines EN , NL , each equal to EK ; and any number FX , XM each equal to FK ;
and ...
Side 224
therefore also the cylinders EB , CM are equal . And because the cylinder FM is
cut by the plane CD parallel to its opposite planes , as the -F K cylinder CM to the
cylinder FD , SO is ( 13. 12. ) the axis LN to the axis KL . But the cylinder CM is ...
therefore also the cylinders EB , CM are equal . And because the cylinder FM is
cut by the plane CD parallel to its opposite planes , as the -F K cylinder CM to the
cylinder FD , SO is ( 13. 12. ) the axis LN to the axis KL . But the cylinder CM is ...
Side 225
consequently ES is a cylinder , the base of which is the circle EFHG , and altitude
MP : and because the cylinder AX is ... is the base ABCD to the base EFGH ; for
the cylinders AX , ES are of the same altitude ; and as the cylinder EO to the ...
consequently ES is a cylinder , the base of which is the circle EFHG , and altitude
MP : and because the cylinder AX is ... is the base ABCD to the base EFGH ; for
the cylinders AX , ES are of the same altitude ; and as the cylinder EO to the ...
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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 |