## 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 |

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Resultat 1-5 av 7

Side 1

COMPANION TO

REMEMBERING OF THE FIRST FOUR BOOKS . WITH A SET OF IMPROVED

FIGURES , AND AN ORIGINAL DEMONSTRATION OF THE PROPOSITION

CALLED ...

COMPANION TO

**EUCLID**: BEING A HELP TO THE UNDERSTANDING ANDREMEMBERING OF THE FIRST FOUR BOOKS . WITH A SET OF IMPROVED

FIGURES , AND AN ORIGINAL DEMONSTRATION OF THE PROPOSITION

CALLED ...

Side 5

COMPANION TO

. The chief design of this work is to afford the beginner in

plan and connexion of argument in the demonstrations he is required to learn ...

COMPANION TO

**EUCLID**. PRELIMINARY OBSERVATIONS AND DIRECTIONS. The chief design of this work is to afford the beginner in

**Euclid**an insight into theplan and connexion of argument in the demonstrations he is required to learn ...

Side 6

Euclides. The learner should keep his Companion open before him while

studying a proposition , and carefully observe the steps of the proof as he

proceeds ; and , in long propositions , he had better draw a line between them in

his

Euclides. The learner should keep his Companion open before him while

studying a proposition , and carefully observe the steps of the proof as he

proceeds ; and , in long propositions , he had better draw a line between them in

his

**Euclid**. Side 7

mon editions of

marked form the immediate object of the proposition ; lines of secondary

importance to these are more faintly traced ; whilst the dotted lines are those

which are merely ...

mon editions of

**Euclid**. It will be seen that the lines which are most stronglymarked form the immediate object of the proposition ; lines of secondary

importance to these are more faintly traced ; whilst the dotted lines are those

which are merely ...

Side 8

What Edition of

can be no doubt that the Symbolical

perspicuous . - - It is the shortest . The propositions in it are in the precise form in

which ...

What Edition of

**Euclid**is used is also a point of importance to the learner . Therecan be no doubt that the Symbolical

**Euclid**is by far the best . It is the mostperspicuous . - - It is the shortest . The propositions in it are in the precise form in

which ...

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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

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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.