## 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 twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |

### Inni boken

Resultat 1-5 av 7

Side 34

For , if it be not parallel , AB and CD being

D , or towards A , C ; let them be

; therefore GEF a 16. 1. is a triangle , and its exterior angle AEF is greater a ...

For , if it be not parallel , AB and CD being

**produced**shall meet either towards B ,D , or towards A , C ; let them be

**produced**and meet towards B , D , in the point G; therefore GEF a 16. 1. is a triangle , and its exterior angle AEF is greater a ...

Side 56

IF a straight line be bisected , and

by the whole line thus

square of half the line bisected , is equal to the square of the straight line which is

...

IF a straight line be bisected , and

**produced**to any point , the rectangle containedby the whole line thus

**produced**, and the part of it**produced**, together with thesquare of half the line bisected , is equal to the square of the straight line which is

...

Side 60

IF a straight line be bisected , and

line thus

double of the square of half the line bisected , and of the square of the line made

up ...

IF a straight line be bisected , and

**produced**to any point , the square of the wholeline thus

**produced**, and the square of the part of it**produced**, are togetherdouble of the square of half the line bisected , and of the square of the line made

up ...

Side 209

G Let AB , BC , two straight lines meeting one another , be parallel to DE , EF ,

that meet one another , but are not in the same plane with AB , BC : the planes

through AB , BC , and DE , EF shall not meet , though

...

G Let AB , BC , two straight lines meeting one another , be parallel to DE , EF ,

that meet one another , but are not in the same plane with AB , BC : the planes

through AB , BC , and DE , EF shall not meet , though

**produced**. From the point B...

Side 210

For , if it is not , EF , GH shall meet , if

first , let them be

since EFK is in the plane AB , every point in K EFK is in that plane : and K is a ...

For , if it is not , EF , GH shall meet , if

**produced**, either on the side of FH , or EG :first , let them be

**produced**on the side of FH , and meet in the point K ; therefore ,since EFK is in the plane AB , every point in K EFK is in that plane : and K is a ...

### 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 Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples 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 opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained 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 30 - Any two sides of a triangle are together greater than the third side.

Side 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...

Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.

Side 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.