## 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 386

The

segment DA of the diameter passing through A , one extremity of the arch AC ,

between the

, or ...

The

**Sine**of a quadrant , or of a right angle , is equal to the radius . V. Thesegment DA of the diameter passing through A , one extremity of the arch AC ,

between the

**sine**CD and that extremity , is called the Versed**Sine**of the arch AC, or ...

Side 403

Pl . Tr . ) ; but AE is the

and the angle AEF is the inclination of the planes CBD , ABD ( 6 . des . 11. ) , or

the spherical angle ABC : therefore the

...

Pl . Tr . ) ; but AE is the

**sine**of the arch AB , and AF the tangent of the arch AC ,and the angle AEF is the inclination of the planes CBD , ABD ( 6 . des . 11. ) , or

the spherical angle ABC : therefore the

**sine**of the arch AB is to the radius , as the...

Side 405

The same construction remaining ; in the triangle CEF , the

hypothenuse CF is to the radius , as the

opposite angle CFE ( 18. of this ) ; that is , in the triangle ABC , the co -

side CA is to ...

The same construction remaining ; in the triangle CEF , the

**sine**of thehypothenuse CF is to the radius , as the

**sine**of the side CE to the**sine**of theopposite angle CFE ( 18. of this ) ; that is , in the triangle ABC , the co -

**sine**of theside CA is to ...

Side 410

of BC is to the

wherefore ( 11. 5. ) the

of BC is to the

**sine**of the angle A as the**sine**of AB to the**sine**of the angle C ;wherefore ( 11. 5. ) the

**sine**of the side AC is to the**sine**of the angle B , as the**sine**of AB to the**sine**of the angle C. Secondly , Let BCD be an oblique angled ... Side 411

For , by 17 , the

the angle B ; and by 17 , and inversion , the radius is to the

tangent of D to the tangent of AC : therefore , ex æquo perturbate , the

is ...

For , by 17 , the

**sine**of BA is to the radius , as the tangent of AC to the tangent ofthe angle B ; and by 17 , and inversion , the radius is to the

**sine**of AD , as thetangent of D to the tangent of AC : therefore , ex æquo perturbate , the

**sine**of BAis ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.