## A companion to Euclid: being a help to the understanding and remembering of the first four books. With a set of improved figures, and an original demonstration of the proposition called in Euclid the twelfth axiom, by a graduate |

### Inni boken

Resultat 1-5 av 5

Side 39

... a reference to number in this case , viz . , to the number of inches , ( or other

units of length ) in the lines AB , BC . For instance , if Al be 5 inches long , and BC

3 inches , and if on each of the small inch - lines into which AB is

square ...

... a reference to number in this case , viz . , to the number of inches , ( or other

units of length ) in the lines AB , BC . For instance , if Al be 5 inches long , and BC

3 inches , and if on each of the small inch - lines into which AB is

**divided**asquare ...

Side 40

...

lines is equal to the G ! rectangles contained by the undivided line , and the

several parts F of the

figures ...

...

**divided**into any number of parts , the rectangle contained by the two straightlines is equal to the G ! rectangles contained by the undivided line , and the

several parts F of the

**divided**line . L H K A - Proved by showing that a X BC * =figures ...

Side 41

If a straight line be

the whole and each of the parts are together equal to the square of the whole line

. Proved by showing that ab % = figures AF + CE ; and that these are = AB X AC ...

If a straight line be

**divided**A Ç B into any two parts , the rectangles contained bythe whole and each of the parts are together equal to the square of the whole line

. Proved by showing that ab % = figures AF + CE ; and that these are = AB X AC ...

Side 43

E Proved by showing that ABS + BCS = figs . Ag + GE + 2 CH + KF , and that

these = 2 AH + KF ; and that these = 2 AB X BC + Ac * . A C LG KKN

PROPOSITION VIII . · Theorem . If a straight line be

four times the ...

E Proved by showing that ABS + BCS = figs . Ag + GE + 2 CH + KF , and that

these = 2 AH + KF ; and that these = 2 AB X BC + Ac * . A C LG KKN

PROPOSITION VIII . · Theorem . If a straight line be

**divided**into any two parts ,four times the ...

Side 88

Prove that if the o be

and AB will contain 3 such parts , and : : their difference Bc will contain 2 such

parts . that : : BC being bisected , Be or EC will contain one such part . that : : if

right ...

Prove that if the o be

**divided**into 15 equal parts , ABC will contain 5 such parts ,and AB will contain 3 such parts , and : : their difference Bc will contain 2 such

parts . that : : BC being bisected , Be or EC will contain one such part . that : : if

right ...

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### Vanlige uttrykk og setninger

alternate angle contained angle equal applied Argument ad absurdum base bisect BOOK centre circumference coincides construction Demonstration described diameter directed divided draw drawn Edition Engravings equal equiangular equilateral Euclid extremities fall figure given circle given point given rectilineal given straight line greater HISTORY impossible inscribe interior joins learner least less meet Nature necessary opposite parallel parallelogram pass pentagon point of contact Problem produced proof PROPOSITION PROPOSITION VIII PROPOSITION XV Proved by showing READINGS rectangle contained right angles right line right Zs segment shows the supposition sides similarly square Steps straight line Suppose supposition is false Theorem touch triangle VOLUME whole whole line YOUNG

### Populære avsnitt

Side 24 - 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, namely, either t}le sides adjacent to the equal...

Side 45 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.

Side 18 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 61 - From this it is manifest that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it, touches the circle...

Side 37 - 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 76 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 77 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.

Side 72 - If a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.

Side 27 - If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side; and also the two interior angles on the same side together equal to two right angles.