## 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]. |

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Resultat 1-5 av 59

Side 113

... together with the second , is to the second , as the third , together with the fourth , is to the fourth . 18th Prop . Book 5 . XVI . Dividendo , by division ; when there are four proportionals ; and it is inferred , that the

... together with the second , is to the second , as the third , together with the fourth , is to the fourth . 18th Prop . Book 5 . XVI . Dividendo , by division ; when there are four proportionals ; and it is inferred , that the

**excess**... Side 114

BOOK V. above the second , as the third to its

BOOK V. above the second , as the third to its

**excess**above the fourth . Prop . E. Book 5 . XVIII . Ex æquali ( sc . distantia ) , or , ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as ... Side 136

Ir four magnitudes be proportionals , they are also proportionals by conversion : that is , the first is to its

Ir four magnitudes be proportionals , they are also proportionals by conversion : that is , the first is to its

**excess**above the second , as the third to its**excess**above the fourth . A Let AB be to BE , as CD to DF ; then BA is to AE ... Side 141

If the same hypothesis be made as in the proposition , the

If the same hypothesis be made as in the proposition , the

**excess**of the first and fifth shall be to the second , 1 a 22. 5 . Book V. as the**excess**of the third and sixth OF EUCLID . 141. Side 142

Book V. as the

Book V. as the

**excess**of the third and sixth to the fourth : The demonstration of this is the same with that of the proposition , if division be used instead of composition . COR . 2. The proposition holds true of two ranks of ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |

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added altitude angle ABC angle BAC arch base Book Book XI centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC Take taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 43 - 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 20 - Any two sides of a triangle are together greater than the third side.

Side 30 - 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 20 - 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 310 - 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 8 - 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 153 - 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 52 - 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 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Side 165 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.