## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |

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Side vi

... of a learned gentleman. To which are also added, the Elements of Plane and

o - THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. s o I. vi PREFACE.

... of a learned gentleman. To which are also added, the Elements of Plane and

**Spherical**Trigonometry, which are commonly taught after the Elements of Euclid.o - THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. s o I. vi PREFACE.

Side 284

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 same 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 289

And if in the lesser

straight lines betwixt the points in which ... of the solid polyhedron in the greater

the ...

And if in the lesser

**sphere**there be described a solid polyhedron , by drawingstraight lines betwixt the points in which ... of the solid polyhedron in the greater

**sphere**meet the superficies of the lesser ; in the same order in which are joinedthe ...

Side 290

have . Let ABC , DEF be two

**SPHERES**have to one another the triplicate ratio of that which their diametershave . Let ABC , DEF be two

**spheres**, of which the diameters are BC , EF . The**sphere**ABC has to the**sphere**DEF the triplicate ratio of that which BC has to EF . Side 291

have that ratio to a greater

LMN has to the

the diameter BC . But as the

have that ratio to a greater

**sphere**LMN : therefore , by inversion , the**sphere**LMN has to the

**sphere**ABC the triplicate ratio of that which the diameter has tothe diameter BC . But as the

**sphere**LMN to ABC , so is the**sphere**DEF to some ...### Hva folk mener - Skriv en omtale

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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: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone 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 greater Greek half join less likewise magnitude 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 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.