## 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 100

Side 8

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**greater**. It is required to cut off from AB , the**greater**, a part equal to C , the less . C From the point A drawa the straight line AD equal to C ; and from the centre A , and at the di- 3 Post . stance AD , describeb the circle DEF ... Side 12

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**greater**than BCD ; much more then is the angle BDC**greater**than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved to be**greater**than the same BCD ; which is impossible ... Side 18

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**greater**than the angle ECF ; therefore the angle ACD is**greater**than BAE : In the same manner , if the side BC be bisected , it may be 15. 1. demonstrated that the angle BCG , that is , the angle ACD , is**greater**than the angle ABC ... Side 19

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**greater**than the angles ABC , ACB ; but ACD , ACB are together equal to two right angles ; therefore the angles ABC ...**greater**side of every triangle is opposite to the**greater**angle . Let ABC be a triangle , of which the side AC is ... Side 20

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**greater**than AB . Wherefore the**greater**angle , & c . Q.E.D. b 18. 1 . PROP . XX . THEOR . See N. ANY two sides of a triangle are together**greater**than the third side . Let ABC be a triangle ; any two sides of it together are**greater**...### 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.