## 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 78

Side 307

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**given**the method of doing : For this reason , we have changed the construction to one , which , without doubt , is Euclid's , in which no- thing is required but to add a**magnitude**to it- self a certain number of times ; and this is to ... Side 312

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**given**the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had**given**, has been deceived in applying what is manifest , when understood of**magnitudes**, unto ratios , viz . that a**magnitude**... Side 330

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**given**rectangle , it is required to apply a rectangle to AB equal to C , D , exceeding by a square . Draw AE , BF ...**magnitude**of it being likewise**given**, to find its sides . And the 4th Problem is the same with this : To find a ... Side 333

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**magnitude**, that are neither similar nor equal , as shall be demonstrated after the notes on the 10th definition ...**given**no definition of equal figures , and it is certain he did not give this ; For what is called the first def ... Side 336

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**magnitude**D which is less than A , B , C , together , will answer the problem . But if B and C together be less than ...**given**of which A and B together are not less than C and D together , and such that any three of them whatever ...### 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.