## 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 227

To describe in the greater of two

polyhedron , the superficies of which shall not meet the lesser

be two

a ...

To describe in the greater of two

**spheres**which have the some centre , a solidpolyhedron , the superficies of which shall not meet the lesser

**sphere**. * Let therebe two

**spheres**about the same centre A ; it is required to describe in the greatera ...

Side 231

And that the other planes between the quadrants BX , KX fall without the lesser

plane of the quadrilateral SOPT , and join IO ; and , as was demonstrated of the

plane ...

And that the other planes between the quadrants BX , KX fall without the lesser

**sphere**, is thus demonstrated ; from the point A draw AI perpendicular to theplane of the quadrilateral SOPT , and join IO ; and , as was demonstrated of the

plane ...

Side 232

divided into the same number of pyramids , and in the same order , the pyramids

shall be similar to one another each to each ; because they have the solid angles

...

**sphere**BCDE has to the diameter of the other**sphere**; for if these two solids bedivided into the same number of pyramids , and in the same order , the pyramids

shall be similar to one another each to each ; because they have the solid angles

...

Side 233

the

solid polyhedron in the

which BC has to EF . But the

ratio of ...

the

**sphere**DEF ; therefore the solid polyhedron in the**sphere**ABC has to thesolid polyhedron in the

**sphere**DEF , the triplicate ratio ( Cor . 17. 12. ) of thatwhich BC has to EF . But the

**sphere**ABC has to the**sphere**GHK , the triplicateratio of ...

Side 396

drawn to the circumference of the circle are equal . II . A great circle of the

is ...

**SPHERICAL**TRIGONOMETRY . DEFINITIONS . 1 . THE pole of a circle of the**sphere**is a point in the superficies of the**sphere**, from which all straight linesdrawn to the circumference of the circle are equal . II . A great circle of the

**sphere**is ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### 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.