## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five Books |

### Inni boken

Side 100

A Less number or

part , or a submultiple of the greater ...

respect of quantity , that is , which are either equal to one another , or unequal ,

are ...

A Less number or

**magnitude**is said to measure a greater , or to be a measure , apart , or a submultiple of the greater ...

**Magnitudes**which can be compared inrespect of quantity , that is , which are either equal to one another , or unequal ,

are ...

Side 104

Ex æquo , inversely ; when there are three or more

others , which taken two and two in a cross order , have the same ratio ; that is ,

when the first

the ...

Ex æquo , inversely ; when there are three or more

**magnitudes**, and as manyothers , which taken two and two in a cross order , have the same ratio ; that is ,

when the first

**magnitude**is to the second in the first rank , as the last but one is tothe ...

Side 105

Divide AB into

equal each of them to F : the number therefore , of the

equal ( hyp . ) to the number of the others AG , GB . And because AG is equal to E

...

Divide AB into

**magnitudes**equal to E , viz . , AG , & 미 GB ; and CD into CH , HD ,equal each of them to F : the number therefore , of the

**magnitudes**CH , HD isequal ( hyp . ) to the number of the others AG , GB . And because AG is equal to E

...

Side 116

D G K Because AB is the same multiple of C , that DE is of F ; there are as many

divided into

D G K Because AB is the same multiple of C , that DE is of F ; there are as many

**magnitudes**in AB each equal to C , as there are in DE each equal to F : let AB bedivided into

**magnitudes**, each equal to C , viz . , AG , GH , HB ; and DE into ... Side 122

With Notes and Illustrations, and an Appendix in Five Books Euclid, James

Thomson. like multiples whatever of A , D , and M , N of C , F : therefore ( V. def . 5

. ) as A : C :: D : F . Next , let there be four

four , E ...

With Notes and Illustrations, and an Appendix in Five Books Euclid, James

Thomson. like multiples whatever of A , D , and M , N of C , F : therefore ( V. def . 5

. ) as A : C :: D : F . Next , let there be four

**magnitudes**, A , B , C , D , and otherfour , E ...

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude base bisected called centre chord circle circumference coincide common cone consequently const construction contained continual cylinder demonstrated describe diagonal diameter difference divided double draw equal equal angles extremities figure fore four fourth given given circle given point given straight line greater half Hence inscribed join less magnitudes manner means meet method multiple opposite parallel parallelepiped parallelogram pass perpendicular plane polygon prism PROB produced proof PROP proportional proposition proved pyramid radius ratio reason rectangle remaining respectively right angles Schol segments semicircle shown sides similar square straight line taken THEOR third touching triangle triangle ABC twice vertical wherefore whole

### Populære avsnitt

Side 94 - 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.

Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - 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.

Side 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...