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]. |
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Side 47
Q. E. D. From this proposition it is manifest , that the difference of the squares of two unequal lines AC , CD , is equal to the rectangle contained by their sum and difference . M Boox II . BOOK II . PROP . VI . THEOR . If OF EUCLID .
Q. E. D. From this proposition it is manifest , that the difference of the squares of two unequal lines AC , CD , is equal to the rectangle contained by their sum and difference . M Boox II . BOOK II . PROP . VI . THEOR . If OF EUCLID .
Side 109
... the circumference ABC , being the third part of the whole , contains five ; and the circumference AB , which is the fifth part of the whole , contains three ; therefore BC their difference contains two of the same parts : Bisect BC ...
... the circumference ABC , being the third part of the whole , contains five ; and the circumference AB , which is the fifth part of the whole , contains three ; therefore BC their difference contains two of the same parts : Bisect BC ...
Side 294
... that he may supply the omission he blames Euclid for , which determination is , that any of the three straight lines must be less than the sum , but greater than the difference of the other two : From this he shows the circles must ...
... that he may supply the omission he blames Euclid for , which determination is , that any of the three straight lines must be less than the sum , but greater than the difference of the other two : From this he shows the circles must ...
Side 308
BOOK V. sharpen one's genius to invent others like it : whereas there is not the least difference between the two demonstrations , except a single word in the construction , which very probably has been owing to an unskilful librarian .
BOOK V. sharpen one's genius to invent others like it : whereas there is not the least difference between the two demonstrations , except a single word in the construction , which very probably has been owing to an unskilful librarian .
Side 321
... merely upon account of " two ratios being interposed betwixt the extremes , that are , equal to one another : so that there is no difference be" twixt the compounding of ratios , and the duplication or " triplication of them which ...
... merely upon account of " two ratios being interposed betwixt the extremes , that are , equal to one another : so that there is no difference be" twixt the compounding of ratios , and the duplication or " triplication of them which ...
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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 arch base Book Book XI centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess 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 310 - 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 |