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The locus of a point which is equidistant from two fixed points is the perpendicular bisector of the straight line joining the two fixed points.
The locus of a point which is equidistant from two intersecting straight lines consists of the pair of straight lines which bisect the angles between the two given lines.
A straight line drawn from the centre of a circle to bisect a chord which is not the diameter is at right angles to the chord; conversely the perpendicular to a chord from the centre bisects the chord.
There is one circle, and one only, which passes through three given points not in a straight line.
In equal circles (or in the same circle) (i) if two arcs subtend equal angles at the centres, they are equal; (ii) conversely, if two arcs are equal they subtend equal angles at the centres.
In equal circles (or in the same circle) (i) if two chords are equal, they cut off equal arcs; (ii) conversely, if two arcs are equal the chords of the arcs are equal.
Equal chords in a circle are equidistant from the centre; and the converse.
The tangents at any point of a circle and the radius through the point are perpendicular to one another.
If two circles touch, the point of contact lies on the straight line through the centres.
The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
Angles in the same segment of a circle are equal; and, if the line joining two points subtends equal angles at two other points on the same side of it, the four points lie on a circle.
The angle in a semi-circle is a right angle, the angle in a segment greater than a semi-circle is less than a right angle, and the angle in a segment less than a semicircle is greater than a right angle.
The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
If two chords of a circle intersect either inside or outside the circle, the rectangle contained by the parts of the one is equal to the rectangle contained by the parts of the other.
PROPORTION: SIMILAR TRIANGLES.
If a straight line is drawn parallel to one side of a triangle, the other two sides are divided proportionally; and the converse.
If two triangles are equiangular, their corresponding sides are proportional; and the converse.
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.
The internal bisector of an angle of a triangle divides the opposite sides internally in the ratio of the sides containing the angle, and likewise the external bisector externally.
The ratio of the areas of similar triangles is equal to the ratio of the squares on corresponding sides.
The following books are suggested for Algebra-
BAKER and BOURNE: Elementary Algebra, Part I.
HALL and STEVENS: A School Geometry, Part I-V is prescribed.
HISTORY AND GEOGRAPHY.
One paper will be set in History and one paper in Geography.
One question in map-drawing will be included in the question-paper in Geography.
English History." A Junior History of England" by M. & C. Oman.
Indian History.-De la Fosse's History of India for High Schools (New Edition).
The following course in Geography is prescribed :General Geography of the world in outline together with India in fuller detail according to the undermentioned syllabus:
A. Elementary Astronomical, Mathematical and Physical Geography.
(i) Shape of the earth-Day and night-The Sea
(ii) Latitude and Longitude-Simple map making, (iii) Surface of the earth-Rainfall and water-partings-Winds, Tides and Currents.
B.-Political Geography of the world in outline.
C.-General Geography of the Indian Empire.
(i) Relief of India.
(ii) Climate and Rainfall.
(iii) Distribution of Population.
(iv) Means of Communication.
(v) Trade and Industries.
(vii) Animals. (viii) Minerals.
Three papers will be set in each of the Classical Languages. The first paper will contain questions on the prescribed course and Grammar. The second paper will contain passages for translation from the Classical Language into English-these passages to be taken not from the prescribed text-books but certain other books recommended for rapid reading. The third paper will contain English sentences or passages to be rendered into the Classical Language. Candidates are required to gain minimum pass-marks in the third paper, and in the three papers combined.
Prescribed Course. -Adityaram Bhattacharya -Sanskrit Siksha. (Selection in Prose and Poetry).
Rajkrishna Banerji - Upakramanika, or any other elementary book in English or in Hindi covering the same ground.
Book recommended for the second paper-Hitopadesha. (Expurgated Ed. by the Indian Press, Allahabad.)
NOTE.-Sanskrit must be written in the Devanagri character.
Prescribed Course.-Shams-ul-ulama M. Syyad Amjad Ali, M.A.: Selections in Arabic Prose and Poetry together with Elements of Arabic Grammar as contained in Mizan Munsha'ib Sarf Mir and Nahv Mir.
Book recommended for the second paper-Nafhatu Yaman (First Chapter).
(c) Persian with Arabic.
Prescribed Course.-Shams-ul-ulama M. Syyad Amjad Ali, M.A.: Entrance Persian Course and First Elements of Arabic Grammar.
Book recommended for the second paper--Saadi's Gulistan.
Prescribed Course.-VIRGIL: Eneid, Books IV and V. CESAR De Bello Gallico, IV and V.
Grammar recommended: Gildersleeve's Latin Gram
Books recommended for the second paper
Prescribed Course.-XENOPHON: Anabasis, Books I, II, III.
Grammar recommended: Rutherford's Greek Gram
Book recommended for the second paper-Xenophon's Anabasis.
Arnold's First Hebrew Book.
Book recommended for the second paper
Psalms, Book V.
Physics and Chemistry.
GREGORY and SIMMONS: Elementary Physics and Chemistry, first stage.
Tulsidasa's Ramayana-Ajodhya Kanda (Indian Press Edition).
Mudrarakshasa, by Harish Chandra (Khadgavilasa
Hindi Balabodha Vyakarana, by P. Madhava Prasda Pathaka, Benares.
Selections by Shams-ul-ulama M. Syyad Amjad Ali,