## 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 4

**Parallel**straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . 1. Let it be granted , that a straight line may be drawn from any one point to any other ... Side 23

For if it be not

For if it be not

**parallel**, AB and CD , being produced , will meet either towards B , D , or towards A , C : let them be pro- C7 duced and meet towards B , D , in the point G ; therefore GEF is a triangle , and its exterior angle AEF is ... Side 24

it may be demonstrated , that they do not meet towards A , C : but those straight lines which meet neither way , though produced ever so far , are

it may be demonstrated , that they do not meet towards A , C : but those straight lines which meet neither way , though produced ever so far , are

**parallel**to one another : therefore AB is**parallel**to CD . Wherefore , if a straight line ... Side 25

Straight lines which are

Straight lines which are

**parallel**to the same straight line , are**parallel**to each other . Let AB , CD be each of them**parallel**to EF : AB shall be**parallel**to CD . Let the straight line GHK cut AB , EF , CD : and because Ghi cuts the ... Side 26

GHF ; therefore also AGK is equal + to GKD : and they are alternate angles ; therefore AB is

GHF ; therefore also AGK is equal + to GKD : and they are alternate angles ; therefore AB is

**parallel*** to CD . Wherefore , straight lines , & c . Q. E. D. PROPOSITION XXXI . PROB .-- To draw a straight line , through a given point ...### 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 |

### Vanlige uttrykk og setninger

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.