## 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

Resultat 1-5 av 5

Side 16

To

in the same . Let AB be a given straight line , and C a point given in it : it is

required to

point D ...

To

**draw**a straight line at right angles to a given straight line , from a given pointin the same . Let AB be a given straight line , and C a point given in it : it is

required to

**draw**a straight line from the point C at right angles to AB . * Take anypoint D ...

Side 33

Produce AD both ways to the points G , H , and through B

. ) to CA , and through F

GBCA , DEFH is a parallelogram ; and they are equal ( 36. 1. ) to one another ...

Produce AD both ways to the points G , H , and through B

**draw**BG parallel ( 31. 1. ) to CA , and through F

**draw**FH parallel to ED : then each of the figures G А D HGBCA , DEFH is a parallelogram ; and they are equal ( 36. 1. ) to one another ...

Side 43

DHG parallel to CE or BF ; and through H

also through A

is equal ( 43. 1. ) to the complement HF , to each of these add DM ; therefore the ...

DHG parallel to CE or BF ; and through H

**draw**KLM parallel to CB or EF ; andalso through A

**draw**AK parallel to CL or BM ; and because the complement CHis equal ( 43. 1. ) to the complement HF , to each of these add DM ; therefore the ...

Side 163

To

A be the given point above the plane BH ; it is required to

straight line perpendicular to the plane BH . In the plane

To

**draw**a straight line perpendicular to a plane , from a given point above it . LetA be the given point above the plane BH ; it is required to

**draw**from the point A astraight line perpendicular to the plane BH . In the plane

**draw**any straight line ... Side 397

the spherical angle BAC . Q. E. D. Cor . If through the point A , two quadrants AB ,

AC be drawn , the point A will be the pole of the great circle BC , passing through

their extremities B , C. Join AC , and

the spherical angle BAC . Q. E. D. Cor . If through the point A , two quadrants AB ,

AC be drawn , the point A will be the pole of the great circle BC , passing through

their extremities B , C. Join AC , and

**draw**AE a straight line to any other point E ...### Hva folk mener - Skriv en omtale

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

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter 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 gles greater Greek half join less likewise manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### 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.