The Elements of Euclid |
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Side 46
Ir a straight line be divided into two equal , and also into two unequal parts ; the
squares of the two unequal parts are together double of the square of half the line
, and of the square of the line between the points of section . Let the straight line ...
Ir a straight line be divided into two equal , and also into two unequal parts ; the
squares of the two unequal parts are together double of the square of half the line
, and of the square of the line between the points of section . Let the straight line ...
Side 48
EG is double of the square of EF : and EF is equal to CD ; wherefore the square
of EG is double of the square of CD : but it was demonstrated , that the square of
EA is double of the square of AC ; therefore the squares of AE , EG are double of
...
EG is double of the square of EF : and EF is equal to CD ; wherefore the square
of EG is double of the square of CD : but it was demonstrated , that the square of
EA is double of the square of AC ; therefore the squares of AE , EG are double of
...
Side 87
to the angle DAC ; therefore the angles CDA , DAC together , are double of the
angle DAC : but BCD is equal to the angles CDA , DAC ; therefore also BCD is
double of DAC , and BCD is equal to each of the angles BDA , DBA ; each
therefore ...
to the angle DAC ; therefore the angles CDA , DAC together , are double of the
angle DAC : but BCD is equal to the angles CDA , DAC ; therefore also BCD is
double of DAC , and BCD is equal to each of the angles BDA , DBA ; each
therefore ...
Side 89
angle FLC : and because KC is equal to CL , KL is double of KC : in the same
manner , it may be shown that HK is double of BK : and because BK is equal to
KC , as was demonstrated , and that KL is double of KC , and HK double of BK ,
HK ...
angle FLC : and because KC is equal to CL , KL is double of KC : in the same
manner , it may be shown that HK is double of BK : and because BK is equal to
KC , as was demonstrated , and that KL is double of KC , and HK double of BK ,
HK ...
Side 101
Take any equimultiples of each of them , as the doubles of each ; then , by def .
5th of this book , if the double of the first be greater than the double of the second
, the double of the third is greater than the double of the fourth ; but if the first be ...
Take any equimultiples of each of them , as the doubles of each ; then , by def .
5th of this book , if the double of the first be greater than the double of the second
, the double of the third is greater than the double of the fourth ; but if the first be ...
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added altitude angle ABC angle BAC base BC is given 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 magnitude given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid sphere square square of BC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 36 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 248 - 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 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 121 - 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 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Side 80 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | The Elements of Euclid |
| Forfatter | Euclid |
| Redaktør | Robert Simson |
| Utgiver | Desilver, Thomas, 1838 |
| Original fra | Harvard University |
| Digitalisert | 29. sep 2005 |
| Lengde | 416 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |