## The Elements of Euclid |

### Inni boken

Side 188

is the solid PL to the solid KO: and therefore as the solid AB to the solid EX, so is

EX to PL, and PL to KO : but if four magnitudes he continual proportionals, the

first is said to have to the fourth, the

second ...

is the solid PL to the solid KO: and therefore as the solid AB to the solid EX, so is

EX to PL, and PL to KO : but if four magnitudes he continual proportionals, the

first is said to have to the fourth, the

**triplicate ratio**of that which it has to thesecond ...

Side 212

to the solid EHPO: but similar solid parallelopipeds have the triplicate (33. 11.)

ratio of that which their homologous sides have: therefore the solid BGML has to

the solid EHPO the

homologous ...

to the solid EHPO: but similar solid parallelopipeds have the triplicate (33. 11.)

ratio of that which their homologous sides have: therefore the solid BGML has to

the solid EHPO the

**triplicate ratio**of that which the side BC has to thehomologous ...

Side 221

of which the base is the polygon HSEOFPGR, and vertex N. Wherefore also the

first of these two last named pyramids has to the other the

which AC has to EG. But by the hypothesis, the cone of which the base is the

circle ...

of which the base is the polygon HSEOFPGR, and vertex N. Wherefore also the

first of these two last named pyramids has to the other the

**triplicate ratio**of thatwhich AC has to EG. But by the hypothesis, the cone of which the base is the

circle ...

Side 232

ratio of their homologous sides. Therefore the pyramid of which the base is the

quadrilateral KBOS, and vertex A, has to the pyramid in the other sphere of the

same order, the

...

ratio of their homologous sides. Therefore the pyramid of which the base is the

quadrilateral KBOS, and vertex A, has to the pyramid in the other sphere of the

same order, the

**triplicate ratio**of their homologous sides, that is of that ratio which...

Side 233

the sphere DEF; therefore the solid polyhedron in the sphere ABC has to the

solid polyhedron in the sphere DEF, the

BC has to EF. But the sphere ABC has to the sphere GHK, the

that ...

the sphere DEF; therefore the solid polyhedron in the sphere ABC has to the

solid polyhedron in the sphere DEF, the

**triplicate ratio**(Cor. 17. 12.) of that whichBC has to EF. But the sphere ABC has to the sphere GHK, the

**triplicate ratio**ofthat ...

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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.