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

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Página 59

Can you

Can you

**find**other three numbers , besides 3 , 4 , and 5 , such that the squares of the less two numbers shall ... Show by a figure that the**area**of a right - angled triangle , whose base is 4 , and perpendicular 3 , is half 4x3 ; i . e ... Página 63

255. Show by a figure how many square yards there are in a square pole . You know how to

255. Show by a figure how many square yards there are in a square pole . You know how to

**find the area**of a rectangle , and you have changed a rectangle into a rhomboid INVENTIONAL GEOMETRY . 63. Página 64

How would you

How would you

**find the area**of a rhombus ? 257. Can you make a right - angled isosceles triangle equal to a square ? 258. Can you make a circle half the size of another circle ? 259. Can you make an equilateral triangle double the size ... Página 69

Show how you would

Show how you would

**find the area**of a reëntrant - angled trapezium . 294. Exhibit to the eye that 1 + 3 + 4 = 1 . 295. Place a circle about a quadrant . If to one extremity of an arc , not greater than that of a quadrant , there be ... Página 78

And as the areas of all these triangles added together would be equal to the area of the circle : To

And as the areas of all these triangles added together would be equal to the area of the circle : To

**find the area**of a circle — multiply the radius which is the perpendicular common to all these imaginary triangles , by the ...### 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.