## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 7

Side 30

Cor . the point F which is the common Vertex of the triangles ; that isa , together

with

right angles , are equal to twice as many right angles as the figure has fides .

CoR .

Cor . the point F which is the common Vertex of the triangles ; that isa , together

with

**four**right angles . Therefore all the angles of the figure , together with**four**right angles , are equal to twice as many right angles as the figure has fides .

CoR .

Side 50

I. RN . but CK is equal o to RN , because they are the complements of the

parallelogram CO ; therefore also BN is equal to GR . and the

, CK , GR , RN , are therefore equal to one another , and so are quadruple of one

of ...

I. RN . but CK is equal o to RN , because they are the complements of the

parallelogram CO ; therefore also BN is equal to GR . and the

**four**rectangles BN, CK , GR , RN , are therefore equal to one another , and so are quadruple of one

of ...

Side 269

5 . are about equal angles AKQ , EMS , because these angles are , Book XII .

each of them , the fame part of

triangle AKQ is similar to the triangle EMS . c . 6.6 . and because it has been

shewn ...

5 . are about equal angles AKQ , EMS , because these angles are , Book XII .

each of them , the fame part of

**four**right angles at the centers K , M ; therefore thetriangle AKQ is similar to the triangle EMS . c . 6.6 . and because it has been

shewn ...

Side 308

That if

than the “ fourth , when the first is greater than the second ; as Clavius

acknowledges in the 16. Prop . of the 5. Book of the Elements . " But tho ' Clavius

makes ...

That if

**four**magnitudes be “ proportionals , the third must necessarily be greaterthan the “ fourth , when the first is greater than the second ; as Clavius

acknowledges in the 16. Prop . of the 5. Book of the Elements . " But tho ' Clavius

makes ...

Side 338

... D , E are not greater than the angles A , B , E. but these last three are less than

are together less than

... D , E are not greater than the angles A , B , E. but these last three are less than

**four**right angles , as has been demonstrated , wherefore also the angles C , D , Eare together less than

**four**right angles , and every two of them are greater than ...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid 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 muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole

### Populære avsnitt

Side 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.

Side 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.

Side 45 - 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 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Side 163 - 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 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.

Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.