## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

### Inni boken

Side 41

BG is equal to A ; and in like manner the rectangle EH is contained by A , EC :

therefore the

two ...

BG is equal to A ; and in like manner the rectangle EH is contained by A , EC :

therefore the

**rectangle contained**by A , BC is equal to the several**rectangles****contained**by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there betwo ...

Side 136

If four straight lines be proportionals , the

equal to the

, F is equal to the

If four straight lines be proportionals , the

**rectangle contained**by the extremes isequal to the

**rectangle contained**by ... so is E to F ; the**rectangle contained**by AB, F is equal to the

**rectangle contained**by CD , E. From the points A , C draw ( 11. Side 137

IF three straight lines be proportionals , the

is equal to the square of the mean : and if the ... Let the three straight lines A , B ,

C be proportionals , viz . as A to B , so B to C ; the

...

IF three straight lines be proportionals , the

**rectangle contained**by the extremesis equal to the square of the mean : and if the ... Let the three straight lines A , B ,

C be proportionals , viz . as A to B , so B to C ; the

**rectangle contained**by A , C is...

Side 153

If an angle of a triangle be bisected by a straight line , which likewise cuts the

base ; the

straight ...

If an 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 of thestraight ...

Side 414

as the

the

as the

**rectangle contained**by half of the radius , and that excess , to the**rectangle****contained**by half the radius , and the versed sine of B ; ( therefore 29. 30. of this )the

**rectangle contained**by the sines of the sides BC , BA is to the square of the ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - 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 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.