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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Resultat 1-5 av 14
Side 190
... cylinder are the circles described by the two revolving opposite sides of the parallelogram . 1 XXIV . Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid ...
... cylinder are the circles described by the two revolving opposite sides of the parallelogram . 1 XXIV . Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid ...
Side 261
... cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the cylinder ; that is , the cylinder ...
... cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the cylinder ; that is , the cylinder ...
Side 262
... cylinder is less than the prism upon the square described about the circle ABCD : Therefore the prism upon the square ABCD of the same altitude with the cylinder , is greater than half of the cylinder . Bisect the circumferences AB , BC ...
... cylinder is less than the prism upon the square described about the circle ABCD : Therefore the prism upon the square ABCD of the same altitude with the cylinder , is greater than half of the cylinder . Bisect the circumferences AB , BC ...
Side 263
... cylinder be less than the triple of the cone . Let it be less , if possible ; therefore , inverse- ly , the cone is greater than the third part of the cylinder . In the circle ABCD describe a square : this square is greater than the ...
... cylinder be less than the triple of the cone . Let it be less , if possible ; therefore , inverse- ly , the cone is greater than the third part of the cylinder . In the circle ABCD describe a square : this square is greater than the ...
Side 264
... cylinder . But this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the cylinder . Therefore this prism is greater than the cylinder of which the base is the circle ABCD . But it is ...
... cylinder . But this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the cylinder . Therefore this prism is greater than the cylinder of which the base is the circle ABCD . But it is ...
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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
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
Populære avsnitt
Side 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.
Side 16 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.