## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

### From inside the book

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Page 377

A

convex Surface , returning into itself ; conti nually varying , in convexity , from the

Circle which bounds it , till it terminates in a Point , As ACD , or ACD . С B D E Der

.

A

**CONE**is a Solid , having but one Plane Surface , which is a Circle ; and aconvex Surface , returning into itself ; conti nually varying , in convexity , from the

Circle which bounds it , till it terminates in a Point , As ACD , or ACD . С B D E Der

.

Page 378

X. A Right

A A Right

angled Triangle , ABC , on either Side containing the Right Angle , as AB , which

...

X. A Right

**Cone**is when the Axe ( AB , ) is perpendicular to the Plane of its Base .A A Right

**Cone**may be conceived to be generated by the revolution of a rightangled Triangle , ABC , on either Side containing the Right Angle , as AB , which

...

Page 399

I. The Superficies of a Right

Radius of the Base . For , they are , respectively , equal to Triangles , whose

Bases are equal to the Circumference of the Base , and Altitudes equal to BD and

C D ...

I. The Superficies of a Right

**Cone**is to its Base , as the side of the**Cone**to theRadius of the Base . For , they are , respectively , equal to Triangles , whose

Bases are equal to the Circumference of the Base , and Altitudes equal to BD and

C D ...

Page 400

The Superficies of a Right Cylinder , is to a Right

Altitudes , as the side of the Cylinder , to half the Side of the

Superficies of the

Side ...

The Superficies of a Right Cylinder , is to a Right

**Cone**, having equal Bases andAltitudes , as the side of the Cylinder , to half the Side of the

**Cone**. For , theSuperficies of the

**Cone**is to its Base , as the Side to the Radius ; or , as half theSide ...

Page 408

I say , the

Figures , as the circumscribing Solid has Faces ; each equal , respectively , to ...

I say , the

**Cone**is equal to the Sphere . B F Dem . For , because the Base of the**Cone**is equal to the Surface of the Sphere , it may be divided into as many planeFigures , as the circumscribing Solid has Faces ; each equal , respectively , to ...

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### Common terms and phrases

ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe

### Popular passages

Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 221 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.

Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.

Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.

Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.

Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.

Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.