The Elements of Euclid: The Errors by which Theon, Or Others, Have Long 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 5
Side 48
And because AC is equal to CE , the square of ĄC is equal to the square of CE ;
therefore the squares of AC , CE , are double of the square of AC : but the square
of AE is equal * to the squares of AC , CE because ACE is a right angle ...
And because AC is equal to CE , the square of ĄC is equal to the square of CE ;
therefore the squares of AC , CE , are double of the square of AC : but the square
of AE is equal * to the squares of AC , CE because ACE is a right angle ...
Side 49
And because EC is equal to CA , the square of EC is equal to the square of " CA ;
therefore the squares of EC , CA are double of the square of CA : but the square
of EA is equal * to the squares of EC , * 47. 1 . CA ; therefore the square of EA is ...
And because EC is equal to CA , the square of EC is equal to the square of " CA ;
therefore the squares of EC , CA are double of the square of CA : but the square
of EA is equal * to the squares of EC , * 47. 1 . CA ; therefore the square of EA is ...
Side 95
1 . fore the angle BFC is double of the angle KFC , and BKC double of FKC : for
the same reason the angle CFD is double of the angle CFL , and CLD double of
CLF : and because the circumference BC is equal to the circumference CD , the ...
1 . fore the angle BFC is double of the angle KFC , and BKC double of FKC : for
the same reason the angle CFD is double of the angle CFL , and CLD double of
CLF : and because the circumference BC is equal to the circumference CD , the ...
Side 111
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 ...
Side 472
may be found . example : let all the sines to 15 degrees be given ; then , by the
preceding analogy , all the sines to 30 degrees For the radius is to double the
cosine of 15 degrees , as the sine of 1 degree is to the difference of the sines of
14 ...
may be found . example : let all the sines to 15 degrees be given ; then , by the
preceding analogy , all the sines to 30 degrees For the radius is to double the
cosine of 15 degrees , as the sine of 1 degree is to the difference of the sines of
14 ...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
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 Euclid 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 proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Side 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.
Side 46 - If 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 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore 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 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Side 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...
Side 169 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Side 97 - 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.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: The Errors by which Theon, Or Others, Have Long 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 |
| Forfatter | Robert Simson |
| Redaktør | Richard Newton Adams |
| oversatt av | Abram Robertson |
| Utgiver | J. Collingwood, 1827 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 513 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |