## 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 38

upon the side subtending the right angle , is equal to the squares

the sides which contain the right angle . Let ABC be a right angled triangle ,

having the right angle BAC ; the square

the ...

upon the side subtending the right angle , is equal to the squares

**described**uponthe sides which contain the right angle . Let ABC be a right angled triangle ,

having the right angle BAC ; the square

**described**upon the side BC is equal tothe ...

Side 90

that FL , FM , FG are each of them equal to FH , or FK ; therefore the five straight

lines FG , FH , FK , FL , FM are equal to one another : wherefore the circle

through the ...

that FL , FM , FG are each of them equal to FH , or FK ; therefore the five straight

lines FG , FH , FK , FL , FM are equal to one another : wherefore the circle

**described**from the centre F , at the distance of one of these five , shall passthrough the ...

Side 150

Let ABC be a right angled triangle , having the right angle BAC ; the rectilineal

figure

upon BA , AC . Draw the perpendicular AD ; therefore , because in the right

angled ...

Let ABC be a right angled triangle , having the right angle BAC ; the rectilineal

figure

**described**upon BC is equal to the similar and similarly**described**figuresupon BA , AC . Draw the perpendicular AD ; therefore , because in the right

angled ...

Side 325

If two rectilineal figures given in species be

, they shall have a given ratio to one another . * Let any two rectilineal figures

ABCDE , ABFG , which are given in species , be

straight ...

If two rectilineal figures given in species be

**described**upon the same straight line, they shall have a given ratio to one another . * Let any two rectilineal figures

ABCDE , ABFG , which are given in species , be

**described**upon the samestraight ...

Side 327

If two straight lines have a given ratio to one another ; the rectilineal figures given

in species

figure AG similar and similarly placed to the figure F ; and because F is given in ...

If two straight lines have a given ratio to one another ; the rectilineal figures given

in species

**described**upon them , shall ... Upon the straight line AB ,**describe**thefigure AG similar and similarly placed to the figure F ; and because F is given in ...

### 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.