## INVENTIONAL GEOMETRY: A SERIES OF PROBLEMS INTENDED TO FAMILIARIZE THE PUPIL WITH GEOMETRICAL CONCEPTIONS, AND TO EXERCISE HIS INVENTIVE FACULTY. |

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angle angular points arithmetic arrange assistance axis base body boundaries breadth calculation called centre circle circumference common cone construct contains cube curve determine diagonal diameter dimensions distance divide a line draw ellipse equal and similar equal sectors equilateral triangle expressed extremities face feet figure find the area five four equal geometry give a sketch Given gles greater half halved height hexagon inches invent isosceles triangle kinds length less line drawn line of chords means measure meet method octagon parallel pentagon perpendicular piece of card place a square plane polygon problems protractor prove pupil pyramid quadrant questions radii radius ratio rectangle regular represent respective rhomboid rhombus right angle right-angled right-angled triangle scale secant sector segment sides sides is called solid square square inches surface takes the name tangent touch trapezium versed sine

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Página 43 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.

Página 13 - I keep the subject constantly before me, and wait till the first dawnings open slowly by little and little into a full and clear light.

Página 23 - ... their centres. \\ Division of Circles. Circles, or arcs, may, like straight lines, have given distances marked off upon them, and may be divided into equal parts. The line which joins the extremities of an arc, is called the chord of that arc. When the arc is very short, its length cannot be ordinarily distinguished from that of its chord. It is ou this principle that any given straight distance may be transferred to a circle or to any curve.

Página 3 - ... TAPPAN, MA ROBINSON'S NEW GEOMETRY AND TRIGONOMETRY. 8vo, calf. 453 pages $1.60 Embracing plane and solid geometry, and plane and spherical trigonometry, with numerous practical problems. SPENCER'S INVENTIONAL GEOMETRY. (Science Primer Series.) By WM. GEO. SPENCER.

Página 4 - To its great efficiency, both as a means of providing interest in geometry, and as a mental discipline, I can give personal testimony. I have seen it create in a class of boys so much enthusiasm that they looked forward to their geometry lesson as a chief event in the week. And girls, initiated in the system by my father, have frequently begged of him for problems to solve during the holidays.

Página 5 - ... or of a kingdom; that a geometry still higher is the foundation of the noble science of the astronomer, who by it not only determines the diameter of the globe he lives upon, but as well the sizes of the sun, moon, and planets, and their distances from us and from each other; when it is considered also, that by this higher kind of geometry, with the assistance of a chart and a mariner's compass, the sailor navigates the ocean with success, and thus brings all nations into amicable intercourse...

Página 22 - ... the outside of the second, write the name of the boundary. In the third, write against the centre its name. And between the centre and the circumference of the fourth circle, draw a few radii and write on each its name. 23. Can you place two circles to touch each other at a particular point ? 24.

Página 47 - PROPOSITION 25. To find the centre of the circle, of which a given arc is a part. Let ABC be a given arc : it is required to find the centre of the circle, of which the arc ABC is a part. CONSTRUCTION. Draw AC, and bisect it at D. (I. Prop. 10.) At D draw DB at right angles to AC cutting the arc at B. (I. Prop. 11.) Draw AB, bisect it at E, and at E draw EF at right angles to AB meeting BD or BD produced at F*; then F is the centre required. PROOF.

Página 34 - When a polygon has all its sides equal and all its angles equal it is called a regular polygon.

Página 2 - In the Office of the Librarian of Congress, at Washington. PREFACE TO THE AMERICAN EDITION.