Books Books If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 117
by Charles Reiner - 1837 - 215 pages ## The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...1. — By making A equal to the whole line considered as divided into two parts, it appears that if a straight line be divided into any two parts, the square of the whole liriiHs equal to the sum of the rectangles contained by the whole line and each of the parts. Cor.... ## Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 690 pages
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided into two equal, and also into two unequal parts ; the... ## Report of Her Majesty's Civil Service Commissioners: Together with ..., Volume 3

1858 - 398 pages
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided into two equal, and also into two unequal parts ; the... ## Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...vertical angle of the triangle and the point of intersection will bisect the vertical angle. 4. If a straight line be divided into any two parts, the...square of the whole line is equal to the squares of the parts and to twice the rectangle contained by the parts. Explain how a rectangle is represented arithmetically,... ## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...THEOREM. If a straight line is divided into any two parts, the square oj the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square on AB is equivalent to the... ## Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...parallelogram which are about the diameter of any parallelogram, are equal to one another. 4. II. If a st. line be divided into any two parts, the square of the whole line equals the square of the two parts together with twice the rectangle contained by the parts. Def. 30.... ## Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858 - 134 pages
...I, Ax. 1. Hyp. Cone. •ui Con e. Def. 1.1 1. .in. I. \x. I. BOOK II. 85 PROP. IV. THEOII. If a st. line be divided into any two parts, the square of the whole line equals the squares of the two parts, together with twice the rectangle contained by the parts. CоN.... ## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...the following equations ,-, 2x + 5 5 2x-5 3 2.a? + 7 2j;-7 __ 1^ ~ 14 21 1 (2) bx-ay=d EUCLID. 1. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 2. In every acute-angled triangle the square of the side subtending either of the acute angles is less... ## A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - Examinations - 1859 - 356 pages
...the features of "parallel lines" and "parallelograms" gained from the first book of Euclid. 3. " If a straight line be divided into any two parts, the square of the whole line is equal to the rectangles contained by the whole and each part." Prove this (1) by geometry ; (2) by algebraic demonstration... 