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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Resultat 1-5 av 23
Side 21
than the angle ACB ; but B С it is not ; therefore the side AC is not less than AB ;
and it has been shown that it is not equal to AB ; therefore AC is greater than AB .
Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides ...
than the angle ACB ; but B С it is not ; therefore the side AC is not less than AB ;
and it has been shown that it is not equal to AB ; therefore AC is greater than AB .
Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . Any two sides ...
Side 24
side is opposite to the greater angle ; the side EG is therefore greater than the
side EF ; but EG is equal to BC ; and therefore also BC is greater than EF . ... If
two triangles have two sides of the one equal to two sides of the other , each to
each ...
side is opposite to the greater angle ; the side EG is therefore greater than the
side EF ; but EG is equal to BC ; and therefore also BC is greater than EF . ... If
two triangles have two sides of the one equal to two sides of the other , each to
each ...
Side 25
to equal angles in each ; then shall the other sides be equal , each to each ; and
also the third angle of the one to the ... ABC to DEF , and BCA to EFD ; also one
side equal to one side ; and first let those sides be equal which are adjacent to ...
to equal angles in each ; then shall the other sides be equal , each to each ; and
also the third angle of the one to the ... ABC to DEF , and BCA to EFD ; also one
side equal to one side ; and first let those sides be equal which are adjacent to ...
Side 36
to two right angles : wherefore the angles BHF , HFE are less than two right
angles : but straight lines which with another straight line make the interior angles
upon the same side less than two right angles , do meet ( 12 . Ax . ) if produced
far ...
to two right angles : wherefore the angles BHF , HFE are less than two right
angles : but straight lines which with another straight line make the interior angles
upon the same side less than two right angles , do meet ( 12 . Ax . ) if produced
far ...
Side 86
Join AC , BD cutting one another in E ; and because DA is equal to AB , and AC
common to the triangles DAC , BAC , the two sides DA , AC are equal to the two
BA , AC ; and А the base DC is equal to the base BC ; whereD fore the angle
DAC ...
Join AC , BD cutting one another in E ; and because DA is equal to AB , and AC
common to the triangles DAC , BAC , the two sides DA , AC are equal to the two
BA , AC ; and А the base DC is equal to the base BC ; whereD fore the angle
DAC ...
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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 |