The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |
Inni boken
Resultat 1-5 av 5
Side 53
1 . fore the square of EA is double of the square of AC : Again , because GF is
equal to FE , the square of GF is equal to the square of FE ; and therefore the
squares of GF , FE are double of the square of EF : But the square of EG is equali
to the ...
1 . fore the square of EA is double of the square of AC : Again , because GF is
equal to FE , the square of GF is equal to the square of FE ; and therefore the
squares of GF , FE are double of the square of EF : But the square of EG is equali
to the ...
Side 91
ĐB two straight lines drawn from it , of which DCA cuts Book IIE . the circle , and
DB touches the same : The rectangle AD , DC is equal to the square of DB .
Either DCA passes through the centre , or it does not ; first , let it pass through the
...
ĐB two straight lines drawn from it , of which DCA cuts Book IIE . the circle , and
DB touches the same : The rectangle AD , DC is equal to the square of DB .
Either DCA passes through the centre , or it does not ; first , let it pass through the
...
Side 328
EF or EG , that is , to ) the squares of ED , DG : Take away the square of DG from
each of these equals ; therefore the . remaining rectangle AG , GB , is equal to the
square of ED , , that is , of C : But the rectangle AG , GB , is the rectangle AH ...
EF or EG , that is , to ) the squares of ED , DG : Take away the square of DG from
each of these equals ; therefore the . remaining rectangle AG , GB , is equal to the
square of ED , , that is , of C : But the rectangle AG , GB , is the rectangle AH ...
Side 438
CB is to the rectangle CB , BD , asa the rectangle HG , GO , to the rectangle HG ,
GL : and the square of CB is equal to the rectangle HG , GO , because GO , BC ,
GH , are prob 14 . 5 . portionals ; therefore the rectangle CB , BD is equal to HG ...
CB is to the rectangle CB , BD , asa the rectangle HG , GO , to the rectangle HG ,
GL : and the square of CB is equal to the rectangle HG , GO , because GO , BC ,
GH , are prob 14 . 5 . portionals ; therefore the rectangle CB , BD is equal to HG ...
Side 465
Next , the magnitude of AC . is exhibited by making the rectangle EG , G # equal
to it ; and the given excess of the square of BC above the square of BA , to which
excess the rectangle CB , BD is equal , is exhibited by the rectangle HG , GL ...
Next , the magnitude of AC . is exhibited by making the rectangle EG , G # equal
to it ; and the given excess of the square of BC above the square of BA , to which
excess the rectangle CB , BD is equal , is exhibited by the rectangle HG , GL ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC Take taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 43 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 20 - Any two sides of a triangle are together greater than the third side.
Side 30 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 20 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Side 306 - 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 8 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.
Side 153 - 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 52 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Side 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.
Bibliografisk informasjon
| Tittel | The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson]. |
| Forfatter | Euclides |
| Redaktør | Robert Simson |
| Utgave | 16 |
| distribuert | 1814 |
| Original fra | Oxford University |
| Digitalisert | 19. apr 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |