## Inventional Geometry: A Series of Problems, Intended to Familiarize the Pupil with Geometrical Conceptions, and to Exercise His Inventive Faculty |

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the boundary is called the circumference of the circle , and the equal lines drawn from the centre to the circumference are called the

the boundary is called the circumference of the circle , and the equal lines drawn from the centre to the circumference are called the

**radii**of the circle . 22. Make four circles . On the first write its name . Around the outside of the ... Página 23

When two

When two

**radii**connect together any two points in the circumference of a circle which are on exactly the opposite sides of the centre , they make a chord , which is called the diameter of the circle , and such diameter divides the ... Página 27

The figure formed by two

The figure formed by two

**radii**and an arc is called a sector . When a circle is divided into four equal sectors , each of such sectors takes the name of quadrant . 50. Divide a circle into four equal sectors , and write upon each sector ... Página 28

When a sector has an arc of 180 ° , the

When a sector has an arc of 180 ° , the

**radii**forming with each other one straight line , it has the same claim to be called a sector as it has to be called a segment , and yet it seldom takes the name of either , being generally called ... Página 31

Can you place two equal sectors so that one corresponding

Can you place two equal sectors so that one corresponding

**radius**of each sector may be in one line , and so that their angles may point 7 ? the same way " Of course it means two lines in the same plane . 73.### Comentarios de la gente - Escribir un comentario

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### Términos y frases comunes

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 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 radii radius ratio rectangle regular represent respective rhomboid rhombus right angle right-angled triangle scale secant sector segment sides sides is called solid square square inches surface symmetrical takes the name tangent touch trapezium versed sine write its name

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

Página 5 - WHEN it is considered that by geometry the architect constructs our buildings, the civil engineer our railways ; that by a higher kind of geometry, the surveyor makes a map of a county 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...

Página 62 - ... equally long and narrow parallel spaces, cut at equal intervals by lines at right angles to them, with a spare end division subdivided similarly, only at right angles to the other divisions, into ten small rectangles, each of which small rectangles, being provided with a diagonal, is called a diagonal scale. 24:6. Make a diagonal scale that shall express a number consisting of three digits. 247. With the assistance of a diagonal scale, construct a plan of a rectangular piece of ground, whose...

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 83 - Can you divide a common triangle into two equal parts by a line parallel to one of its 376. Can you divide a triangle into two equal parts by a line from any point in any one of its sides ? 377. Show how many solid feet there are in a solid yard. 378. Make an oblique square prism with two rectangular sides and two rhomboidal sides. 379. Make an oblique square prism with all its sides...

Página 5 - INTRODUCTION. it is considered that by geometry the architect constructs our buildings, the civil engineer our railways; that by a higher kind of geometry, the surveyor makes a map of a county 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...

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 47 - Make of one piece of card a hollow octahedron : show how you arrange the surfaces go as to fold together correctly; and give a sketch of the octahedron. 162. Can you divide an angle into four equal angles, without using more than four circles ? 163. In how many ways can you divide an equilateral triangle into three parts, that shall be equal to each other, and similar to each other ? 164. Given an arc of a circle : it is required to find the centre of the circle of which it is an arc. 165. Can you...

Página 2 - Congress, to the year 1876, BY D. APPLETON & CO., In the Office of the Librarian of Congress, at Washington. PREFACE TO THE AMERICAN EDITION. THIS little book, prepared by an experienced mathematical teacher for the use of his own pupils, is based upon the principle that the best and only true education is self-education.