## 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 33

AE parallel to BC , and

EBC , because it is upon the same base BC , and between the same parallels BC

...

**Join**AD ; AD is parallel to BC : for , if it is not , through the point A draw ( 31. 1. )AE parallel to BC , and

**join**EC ; the triangle ABC is equal ( 37. 1. ) to the triangleEBC , because it is upon the same base BC , and between the same parallels BC

...

Side 60

If two circles touch each other internally , the straight line which

being produced shall pass through the ... being produced passes through the

point A. For , if not , let it fall otherwise , if possi- H ble , as FGDH , and

AG ...

If two circles touch each other internally , the straight line which

**joins**their centresbeing produced shall pass through the ... being produced passes through the

point A. For , if not , let it fall otherwise , if possi- H ble , as FGDH , and

**join**AF ,AG ...

Side 72

THEOR . In equal circles equal circumferences are subtended by equal straight

lines . Let ABC , DEF be equal circles , and let the circumferences BGC , EHF

also be equal ; and

EF .

THEOR . In equal circles equal circumferences are subtended by equal straight

lines . Let ABC , DEF be equal circles , and let the circumferences BGC , EHF

also be equal ; and

**join**BC , EF : the straight line BC is equal to the straight lineEF .

Side 363

angle , is given ; and the angle AEC is given ; therefore ( 43. dat . ) the triE angle

ACE is given in species , and the raD tio of EA to AC is therefore given ; and EA ...

**join**AD and produce it to E , and**join**EC : the angle ACE being a B right ( 31. 3. )angle , is given ; and the angle AEC is given ; therefore ( 43. dat . ) the triE angle

ACE is given in species , and the raD tio of EA to AC is therefore given ; and EA ...

Side 397

spherical angle BAC , and the arch BC is called the measure of the spherical

angle BAC . Let the planes of the great circles AB , AC intersect one another in

the straight line AD passing through D their common centre ;

A is ...

spherical angle BAC , and the arch BC is called the measure of the spherical

angle BAC . Let the planes of the great circles AB , AC intersect one another in

the straight line AD passing through D their common centre ;

**join**DB , DC . SinceA is ...

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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.