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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Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 112
... proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
... proportion , is the similitude of ratios . IX . Proportion consists in three terms at least . X. When three magnitudes are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second ...
Σελίδα 113
... proportion- als , and it is inferred , that the second is to the first , as the fourth to the third . Prop . B. Book 5 . XV . Componendo , by composition ; when there are four propor- tionals , and it is inferred , that the first ...
... proportion- als , and it is inferred , that the second is to the first , as the fourth to the third . Prop . B. Book 5 . XV . Componendo , by composition ; when there are four propor- tionals , and it is inferred , that the first ...
Σελίδα 114
... proportion . It is demon- strated in 22d Prop . Book 5 . XX . Ex æquali in proportione perturbata seu inordinata , from equality in perturbate or disorderly proportion . * This term is used when the first magnitude is to the second of ...
... proportion . It is demon- strated in 22d Prop . Book 5 . XX . Ex æquali in proportione perturbata seu inordinata , from equality in perturbate or disorderly proportion . * This term is used when the first magnitude is to the second of ...
Σελίδα 141
... proportion- als , they shall likewise be proportionals F H CDF a 22. 5 . when taken jointly b ; as therefore AG is to GB , so is DH 18. 5 . to HE : but as GB to C , so is HE to F. Therefore ex æqualia , as AG is to C , so is DH to F ...
... proportion- als , they shall likewise be proportionals F H CDF a 22. 5 . when taken jointly b ; as therefore AG is to GB , so is DH 18. 5 . to HE : but as GB to C , so is HE to F. Therefore ex æqualia , as AG is to C , so is DH to F ...
Σελίδα 142
... proportion- als , viz . AB to CD , as E to F ; and let AB be the greatest A. & 14.5 . of them , and consequently F the least . AB , together with F , are greater than CD , together with E. Take AG equal to E , and CH equal to F : Then ...
... proportion- als , viz . AB to CD , as E to F ; and let AB be the greatest A. & 14.5 . of them , and consequently F the least . AB , together with F , are greater than CD , together with E. Take AG equal to E , and CH equal to F : Then ...
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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.