## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 7

Side 100

to D, and of A and C certain equimultiples have been taken, viz. K and L; and of B

and D certain equimultiples G, H; therefore if K be greater than G, L is greater ...

**fore**, that K is the same multiple of A, that L is of C: and because A is to B, as C isto D, and of A and C certain equimultiples have been taken, viz. K and L; and of B

and D certain equimultiples G, H; therefore if K be greater than G, L is greater ...

Side 154

... because they are in the same segment; therefore the triangle ABD is

equiangular to the triangle BCE; where- B

DA; and consequently the rectangle BC, AD is equal (16. 6.) to the rectangle BD,

CE: again, ...

... because they are in the same segment; therefore the triangle ABD is

equiangular to the triangle BCE; where- B

**fore**(4.6.) as BC is to CE, so is BD toDA; and consequently the rectangle BC, AD is equal (16. 6.) to the rectangle BD,

CE: again, ...

Side 185

LQ, so the base CD to D |G K to the base LQ, as be- O L - Q

there- B

- A S H T LR; and therefore the solid AE is equal (9.5.) to the solid CF. But let the

...

LQ, so the base CD to D |G K to the base LQ, as be- O L - Q

**fore**was proved:there- B

**fore**as the solid AE to - the solid LR, so is the C L So solid CF to the solid- A S H T LR; and therefore the solid AE is equal (9.5.) to the solid CF. But let the

...

Side 209

... K B C G H * This may be explained the same way as the like at the mark fin

prop. 2. + See Note.

XIi. THE ELEMENTS OF EUCLID, 209 the solid Q is greater than the prisms in the

...

... K B C G H * This may be explained the same way as the like at the mark fin

prop. 2. + See Note.

**fore**, since the triangle ABC is to the triangle FGH, 27 BOOKXIi. THE ELEMENTS OF EUCLID, 209 the solid Q is greater than the prisms in the

...

Side 336

and K is given, where- M

parallelogram AC is to the parallelogram EG, as the straight line K to the straight

line M, as is demonstrated in the 23d prop. of B. 6. Elem.; therefore the ratio of AC

to EG is ...

and K is given, where- M

**fore**(1.dat) the ratio of K to M is given: but theparallelogram AC is to the parallelogram EG, as the straight line K to the straight

line M, as is demonstrated in the 23d prop. of B. 6. Elem.; therefore the ratio of AC

to EG is ...

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

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

### Vanlige uttrykk og setninger

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore

### 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.