Sidebilder
PDF
ePub
[merged small][merged small][ocr errors][ocr errors][ocr errors][merged small][merged small][merged small][merged small]
[ocr errors]

someone every t om to

[ocr errors]

........ .........

[ocr errors]

............

II ...............

I 2 .... 13 ..

II ..... I2 ..... 13 ... 14 ............... 15 ...............

......... 17 ... ... ... ......

........

5 com begge Feu ce año votter yt. Nam

to bot

14

.........

BOOK II.

19 .... 20 .... 21 .......

[blocks in formation]

...........

...........

............... 26 ... 3 and Sup. (25) 27 ............... 20

.................. 20
...... Sup. (21)

.. Sup. (22)

.. Lemma. .......... 24, 30 ............... 23

...... I ............... I ........... I

2 or a 2 orc

2 orc ........, 2 or 0

......... 2 or 9 ........, 2 or I. m IO .........2 or I. m II ..... I 2 ...

........

[ocr errors]
[ocr errors]

14 ........

d (v1,5) 36 ... ... ...e (V1, 5)

.......... e (v1.5)

xiii

TABLE II. For Comparison with Euclid.

Euclid. E.G. | Euclid. E.G. | Euclid. E.G. Book IV.

BOOK VI. Book XI. Sol. Geo. I ......... 0 (v. I)

.............. 1 2 ... ... ... ... 2, 3

...............

[ocr errors]

ovat ene na

5 5 o o con gent Denn

[ocr errors]

navage

10..

[ocr errors]

IO ............ II. C
II ... 10 and 111. K

............... II 13 ............... 13 14 ............... 12 15 ... 10 and 111. H 16 ... 10 and 111.L

IO ...
II .....
I2 ....

iii.
rov so on.com gener noe som et stort A WNLO

II ...
I 2 ...
13 ...

o

[ocr errors]

14 ...

14 ...

[ocr errors]
[ocr errors][ocr errors]

......

605 Gent to p

[ocr errors]

BOOK V.

[ocr errors]

...

[blocks in formation]
[ocr errors]

BOOK XII. BOOK VI.

.......

I .............., II 2 ............... 12

.?

16 .................
22 ......... 12, 13

............... 31 ..

.......... 32.

[blocks in formation]
[ocr errors]

.........

SCHEME FOR EXAMINATION ON GEOMETRY.

Extent of Examination.

Proofs allowed. All those portions off Proofs of Euclid or others Euclid required by the Uni- depending on previous proversities.

{positions of Euclid.

Also those Propositions In the proofs sent up (if on Proportion required for not Euclid's Book V.) the Euclid VI, XI, XII, estab- Definitions and Enunciations lished for the particular Geo- of previous Theorems on metrical magnitudes to which Proportion made use of to they are applied.

Lbe stated.

With regard to Euc. 1. Any proofs allowed, the 29, 30.

*Axiom or Lemma on which (they depend being stated.

s Any proofs allowed, the With regard to Euc. VI.

Definition or test of Pro1. 33.

Lportion being stated.

N.B. When the Examiner wishes for other proofs than the above, the necessary restrictions and allowable assumptions may be given in the question.

PRELIMINARY NOTICES.

The following symbols will be used simply in lieu of the words to which they are here prefixed.

z angle.
A triangle.
O parallelogram.
o circle.
Oce circumference.
I perpendicular (to).
!! parallel.

+ together with.
= equal to.
>greater than.
< less than.
.:: because.
.:therefore.
: is to.

The object aimed at is merely to place before the student the various steps of an argument in a more succinct form by curtailing the verbiage, thus enabling him to take in at a glance the outline of a proof. It must however be borne in mind that the words themselves must be substituted in any examinations in which symbols are objected to. It will be assumed as self-evident that:

Things which are equal to the same thing are equal to one another.

The whole is equal to the sum of its parts.
If equals be added to equals the wholes are equal.
If equals be taken from equals the remainders are equal.
If equals be added to unequals the wholes are unequal.

If equals be taken from unequals the remainders are unequal.

Things which are double of equal things are equal to one another.

Things which are halves of equal things are equal to one another.

Equimultiples of equal things are equal.

Things, of which the equimultiples are equal, are themselves equal.

If one magnitude be greater than another any multiple of the former is greater than the same multiple of the latter.

If a multiple of one magnitude be greater than the same multiple of another then the former magnitude is greater than the latter.

ERRATA.

P. 12, l. 7, for equal circles read Os having equal radii. , 24, 1. 10 and p. 27, 1. 20, 22, for has been read is.

38, l. 4, for FE read FG.
71, ,, 13, 16. For definitions, see p. 86.

107, , 6, for divides read divide. , 129, , 1, add if possible, let them bisect each other; , 131, , 13, omit to it. » 201. In the diagram the diagonal of 0 FB is AC.

« ForrigeFortsett »