## 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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Side 101

Magnitudes which have the same ratio are called

Magnitudes which have the same ratio are called

**proportionals**. · N . B. When four magnitudes are**proportionals**, it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII . Side 102

In

In

**proportionals**, the antecedent terms are called homologous to one another , as also the consequents to one another . See N. • Geometers make use of the following technical words , to signify certain ways of changing either the order ... Side 103

Convertendo , by conversion ; when there are four

Convertendo , by conversion ; when there are four

**proportionals**, and it is inferred , that the first is to its excess above the second , as the third to its excess above the fourth . Prop . E. Book 5 . XVIII . Side 110

If four magnitudes are

If four magnitudes are

**proportionals**, they are**proportionals**also when taken inversely . Let A be to B , as C is to D : then also inversely B shall be to A , as D to C. Take of B and D , any equimultiples whatever E and F ; and of A ... Side 115

If any number of magnitudes be

If any number of magnitudes be

**proportionals**, as one of the antecedents is to its consequent , so shall all the antecedents taken together , be to all the consequents . Let any number of magnitudes A , B , C 1 2 BOOK V. 115 PROP . XI .### 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 - 1814 |

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added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid 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 manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced Prop proportionals PROPOSITION proved pyramid Q. E. D. PROPOSITION radius reason rectangle rectangle contained remaining right angles segment shewn sides similar sine solid solid angle sphere square square of BC taken third triangle ABC wherefore whole

### Populære avsnitt

Side 32 - To a given straight line, to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle...

Side 138 - 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 39 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...

Side 41 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Side 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...

Side 38 - IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...

Side 262 - 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 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...

Side 165 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.