## 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 141

Wherefore ,

proved , that

another in the duplicate ratio of their homologous sides , and it has already been

...

Wherefore ,

**similar**polygons , & c . Q. E. D. COR . 1. In like manner , it may beproved , that

**similar**four sided figures , or of any number of sides , are one toanother in the duplicate ratio of their homologous sides , and it has already been

...

Side 147

X To a given straight line to apply a parallelogram equal to a given rectilineal

figure , and deficient by a parallelogram

given rectilineal figure to which the parallelogram to be applied is to be equal ,

must ...

X To a given straight line to apply a parallelogram equal to a given rectilineal

figure , and deficient by a parallelogram

**similar**to a given parallelogram : but thegiven rectilineal figure to which the parallelogram to be applied is to be equal ,

must ...

Side 148

the parallelogram EL

parallelogram GH equal to EL and C together , and

to D ; wherefore GH is

FL ...

the parallelogram EL

**similar**and similarly situated to D : and make ( 25. 6. ) theparallelogram GH equal to EL and C together , and

**similar**and similarly situatedto D ; wherefore GH is

**similar**to EL ( 21. 6. ) ; let KH be the side homologous toFL ...

Side 205

and

equal and

the triangle AEG , and of which the vertex is the point H , is equal ( C. 11. ) ...

and

**similar**to the triangle , KDL ; for the same reason the triangle AEG is alsoequal and

**similar**to the triangle HKL . Therefore the pyramid of which the base isthe triangle AEG , and of which the vertex is the point H , is equal ( C. 11. ) ...

Side 212

to BC as DE to EF ; that is , the sides about the equal angles are proportionals ;

wherefore the parallelogram BM is

parallelogram BN is

parallelograms ...

to BC as DE to EF ; that is , the sides about the equal angles are proportionals ;

wherefore the parallelogram BM is

**similar**to EP : for the same reason , theparallelogram BN is

**similar**to ER , and BK to EX ; therefore the threeparallelograms ...

### 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.