## 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 25

to equal angles in each ; then shall the other sides be equal , each to each ; and

also the

two triangles which have the angles ABC , BCA equal to the angles DEF , EFD ,

viz ...

to equal angles in each ; then shall the other sides be equal , each to each ; and

also the

**third**angle of the one to the**third**angle of the other . Let ABC , DEF betwo triangles which have the angles ABC , BCA equal to the angles DEF , EFD ,

viz ...

Side 94

N. B. • When four magnitudes are proportionals , it is usually expressed by saying

, the first is to the second , as the

equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of

the first is ...

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 . When of theequimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of

the first is ...

Side 99

If the first of four magnitudes has the same ratio to the second which the

to the fourth , then any equimultiples whatever of the first and

same ratio to any equimultiples of the second and fourth , viz . the equimultiple ...

If the first of four magnitudes has the same ratio to the second which the

**third**hasto the fourth , then any equimultiples whatever of the first and

**third**shall have thesame ratio to any equimultiples of the second and fourth , viz . the equimultiple ...

Side 168

IF two planes cutting one another be each of them perpendicular to a

their common section shall be perpendicular to the same plane . Let the two

planes AB , BC be each of them perpendicular to a

...

IF two planes cutting one another be each of them perpendicular to a

**third**plane ;their common section shall be perpendicular to the same plane . Let the two

planes AB , BC be each of them perpendicular to a

**third**plane , and let BD be the...

Side 170

than the

same reason , the two plane angles at A each of the points C , D , E , F , viz . the

angles which are at the bases of the triangles , having the common vertex A , are

...

than the

**third**, the angles CBA , ABF , are greater than the angle FBC : for thesame reason , the two plane angles at A each of the points C , D , E , F , viz . the

angles which are at the bases of the triangles , having the common vertex A , are

...

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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.