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].1814 |
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Σελίδα
... BOOKS , ARE CORRECTED , AND SOME OF EUCLID'S DEMONSTRATIONS ARE RESTORED . 1 ALSO THE BOOK OF EUCLID'S DATA , IN LIKE MANNER CORRECTED . By ROBERT SIMSON , M.D. Emeritus Professor of Mathematics in the University of Glasgow . THE ...
... BOOKS , ARE CORRECTED , AND SOME OF EUCLID'S DEMONSTRATIONS ARE RESTORED . 1 ALSO THE BOOK OF EUCLID'S DATA , IN LIKE MANNER CORRECTED . By ROBERT SIMSON , M.D. Emeritus Professor of Mathematics in the University of Glasgow . THE ...
Σελίδα
... Book , in place of the legitimate one which Euclid had given ; and by taking out of this Book , besides other things , the good de- finition which Eudoxus or Euclid had given of compound ratio , and giving an absurd one in place of it ...
... Book , in place of the legitimate one which Euclid had given ; and by taking out of this Book , besides other things , the good de- finition which Eudoxus or Euclid had given of compound ratio , and giving an absurd one in place of it ...
Σελίδα
Euclides Robert Simson. 66 among the Definitions of the 5th Book , by which the doc- trine of compound ratios is rendered plain and easy . Be- sides , among the Definitions of the 11th Book , there is this , which is the tenth , viz ...
Euclides Robert Simson. 66 among the Definitions of the 5th Book , by which the doc- trine of compound ratios is rendered plain and easy . Be- sides , among the Definitions of the 11th Book , there is this , which is the tenth , viz ...
Σελίδα
... Book . Also the Note on the 29th Proposition , Book 1st , is altered , and made more explicit , and a more general Demonstration is given , instead of that which was in the Note on the 10th Definition of Book 11th ; besides , the ...
... Book . Also the Note on the 29th Proposition , Book 1st , is altered , and made more explicit , and a more general Demonstration is given , instead of that which was in the Note on the 10th Definition of Book 11th ; besides , the ...
Σελίδα
... Book I. See Notes . A plane superficies is that in which any two points being See N. taken , the straight line between them lies wholly in that superficies . VIII . " A plane angle is the inclination of two lines to one ano- See N ...
... Book I. See Notes . A plane superficies is that in which any two points being See N. taken , the straight line between them lies wholly in that superficies . VIII . " A plane angle is the inclination of two lines to one ano- See N ...
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ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 3-7 - 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.
Σελίδα 16 - Any two sides of a triangle are together greater than the third side.
Σελίδα 26 - 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.
Σελίδα 16 - 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...
Σελίδα 304 - 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.
Σελίδα 4 - 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.
Σελίδα 147 - 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.
Σελίδα 3-16 - 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.
Σελίδα 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.