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 5
Side 124
Produce BD both ways to the points H , L , and take any number of straight lines
BG , GH , each equal to the base BC ; and DK , KL , any number of them , each
equal to the base CD , and join AG , AH , AK , AL : then , because CB , BG , GH
are ...
Produce BD both ways to the points H , L , and take any number of straight lines
BG , GH , each equal to the base BC ; and DK , KL , any number of them , each
equal to the base CD , and join AG , AH , AK , AL : then , because CB , BG , GH
are ...
Side 190
Ň Next , let the bases EH , NP not be equal ; but EH greater than the other : since
then the solid AB is equal to the solid CD ... Make F then CT equal to AG , and
G T complete the solid parallelopiped CV of which the base L P is NP , and the ...
Ň Next , let the bases EH , NP not be equal ; but EH greater than the other : since
then the solid AB is equal to the solid CD ... Make F then CT equal to AG , and
G T complete the solid parallelopiped CV of which the base L P is NP , and the ...
Side 191
is the solid AB to the solid CV ; for the solids AB , CV are of the same altitude ;
and as MC to CT , so is the base MP to the base PT , and the solid GD to the solid
( 25. 11. ) CV : and therefore as the solid AB to the solid CV , so is the solid CD to
...
is the solid AB to the solid CV ; for the solids AB , CV are of the same altitude ;
and as MC to CT , so is the base MP to the base PT , and the solid GD to the solid
( 25. 11. ) CV : and therefore as the solid AB to the solid CV , so is the solid CD to
...
Side 209
Therefore the base ABC is not to the base DEF , as the pyramid ABCG to any
solid which is less than the pyramid DEFH . In the same manner it may be
demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH
to any ...
Therefore the base ABC is not to the base DEF , as the pyramid ABCG to any
solid which is less than the pyramid DEFH . In the same manner it may be
demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH
to any ...
Side 210
are all the other antecedents to their common consequent : that is as the base
ABCDE to the base FGH , so is the pyramid ABCDEM to the pyramid FGHN : and
, for the same reason , as the base FGHKL to the base FGH , so is the pyramid ...
are all the other antecedents to their common consequent : that is as the base
ABCDE to the base FGH , so is the pyramid ABCDEM to the pyramid FGHN : and
, for the same reason , as the base FGHKL to the base FGH , so is the pyramid ...
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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 |