## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |

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Side xi

... on the Fifth Definition of the Fifth Book about Magnitudes having the same

... on the Fifth Definition of the Fifth Book about Magnitudes having the same

**Ratio**, viz . that this Definition does really extend to commensurable ... Side xii

... and the Third and Fourthi Terms of Two equal

... and the Third and Fourthi Terms of Two equal

**Ratios**, or Four Proportionals ... i . e . the former such as have a**Ratio**, or may be compared together ... Side 205

**Ratio**is a certain mutual relation of two magnitudes to one another of the same kind , according to quantity b . 4. Magnia It might perhaps be better to ... Side 206

Magnitudes are said to have a

Magnitudes are said to have a

**ratio**to one another , which being multiplied can exceed each other . 5. Four magnitudes are said to be in the fame**ratio**... Side 207

Magnitudes which are in , or have the same

Magnitudes which are in , or have the same

**ratio**, are called proportionals . N. B. When four magnitudes are proportionals it is usually expressed by saying ...### Hva folk mener - Skriv en omtale

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A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore four fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe

### Populære avsnitt

Side 247 - 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 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.

Side 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Side 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.

Side 56 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...

Side 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Side 130 - When you have proved that the three angles of every triangle are equal to two right angles...

Side 183 - FK : in the same manner it may be demonstrated, 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...