## 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 |

### Inni boken

Resultat 1-5 av 39

Side 111

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**equimultiples**whatsoever of the first and third being taken , and any**equimultiples**whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ... Side 112

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**equimultiples**of four magnitudes ( taken as in the fifth definition ) , the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said ... Side 114

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**EQUIMULTIPLES**of the same , or of**equal**magnitudes , are**equal**to one another . 4 Prop . lib . 2. Archimedis de sphæra et cylindro . II . Those magnitudes of which the same , or 114 THE ELEMENTS. Side 115

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**equimultiples**, are**equal**to one another . III . A multiple of a greater magnitude is greater than the same multiple ...**equimultiples**of as many , each of each ; what multiple soever any one of them is of its part , the same multiple ... Side 117

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**equimultiples**, these shall be**equimultiples**, the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C , let the**equimultiples**EF ...### Andre utgaver - Vis alle

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.