## 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 405

... a Circle whose Radius is equal to the Diameter , AB , is equal to the

a Sphere , described by the revolution of the Semicircle ADB . But , Circles are to

each other , or amongst themselves , as Squares of their Diameters , Cor . 1. 14.

... a Circle whose Radius is equal to the Diameter , AB , is equal to the

**Surface**ofa Sphere , described by the revolution of the Semicircle ADB . But , Circles are to

each other , or amongst themselves , as Squares of their Diameters , Cor . 1. 14.

Page 406

с EX G If a Sphere be inscribed in a Cylinder , and being both cut by Planes ,

parallel to the Bases of the Cylinder ; each Segment of the spherical

be equal to the portion of the cylindrical , intercepted between the same parallel ...

с EX G If a Sphere be inscribed in a Cylinder , and being both cut by Planes ,

parallel to the Bases of the Cylinder ; each Segment of the spherical

**Surface**willbe equal to the portion of the cylindrical , intercepted between the same parallel ...

Page 407

Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...

Thomas Malton. Cor . The Segments of a spherical

parallel Circles , have the fame Ratio , between themselves , as the Segments ...

Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...

Thomas Malton. Cor . The Segments of a spherical

**Surface**, intercepted betweenparallel Circles , have the fame Ratio , between themselves , as the Segments ...

Page 408

For , because the Base of the Cone is equal to the

be divided into as many plane Figures , as the circumscribing Solid has Faces ;

each equal , respectively , to the other . Consequently , if Right Lines be drawn ...

For , because the Base of the Cone is equal to the

**Surface**of the Sphere , it maybe divided into as many plane Figures , as the circumscribing Solid has Faces ;

each equal , respectively , to the other . Consequently , if Right Lines be drawn ...

Page 22

For , it is equal to a cylindrical

holds true of any portion of the

Planes . The spherical

therefore ...

For , it is equal to a cylindrical

**Surface**of those Dimensions - 16.8 . The sameholds true of any portion of the

**Surface**of a Sphere , intercepted between parallelPlanes . The spherical

**Surface**, intercepted between parallel Planes , istherefore ...

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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.