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 215
cone . fore if each of the circumferences be divided into two equal parts , and
straight lines be drawn from the points of division to the extremities of the
circumferences , and upon the triangles thus made , prisms be erected of the
same altitude ...
cone . fore if each of the circumferences be divided into two equal parts , and
straight lines be drawn from the points of division to the extremities of the
circumferences , and upon the triangles thus made , prisms be erected of the
same altitude ...
Side 216
cone , which together shall be less than the excess of the cone above the third
part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD ,
DH , HA . Therefore the rest of the cone , that is , the pyramid , of which the base
is ...
cone , which together shall be less than the excess of the cone above the third
part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD ,
DH , HA . Therefore the rest of the cone , that is , the pyramid , of which the base
is ...
Side 218
the base is the other polygon , and its vertex N : therefore , as the cone AL to the
solid X , so is the pyramid of which the base is the polygon ATBYCVDQ , and
vertex L , to the pyramid the base of which is the polygon EOFPGRHS , and
vertex N ...
the base is the other polygon , and its vertex N : therefore , as the cone AL to the
solid X , so is the pyramid of which the base is the polygon ATBYCVDQ , and
vertex L , to the pyramid the base of which is the polygon EOFPGRHS , and
vertex N ...
Side 221
But by the hypothesis , the cone of which the base is the circle ABCD , and vertex
L , has to the solid X , the triplicate ratio of that which AC has to EG : therefore as
the cone of which the base is the circle ABCD , and vertex L , is to the solid X ...
But by the hypothesis , the cone of which the base is the circle ABCD , and vertex
L , has to the solid X , the triplicate ratio of that which AC has to EG : therefore as
the cone of which the base is the circle ABCD , and vertex L , is to the solid X ...
Side 222
ABCDL , so is the cone EFGHN to some solid , which must be less ( 14. 5. ) than
the cone ABCDL , because the solid Z is greater than the cone EFGHN : therefore
the cone EFGHN has to a solid which is less than the cone ABCDL , the ...
ABCDL , so is the cone EFGHN to some solid , which must be less ( 14. 5. ) than
the cone ABCDL , because the solid Z is greater than the cone EFGHN : therefore
the cone EFGHN has to a solid which is less than the cone ABCDL , 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 |