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

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Page 11

A PLANE

same Plone . 2. Any Line , between two adiacent Angles , forming or bounding a

A PLANE

**FIGURE**is a Space bounded on all sides by one or more Lines in thesame Plone . 2. Any Line , between two adiacent Angles , forming or bounding a

**Figure**, is called a SIDE of that**Figure**. N. B. If a Plane**Figure**be bounded by ... Page 14

A PLANE

same Plane . 2. Any Line , between two adjacent Angles , forming or bounding a

A PLANE

**FIGURE**is a Space bounded on all sides by one or more Lines in thesame Plane . 2. Any Line , between two adjacent Angles , forming or bounding a

**Figure**, is called a Side of that**Figure**. N. B. If a Plane**Figure**be bounded by ... Page 211

A Right - lined

circumscribing it , when every Angle of the

the circumscribing Circle . 2. A Right - lined

a ...

A Right - lined

**Figure**is said to be inscribed , in a Circle , or to have a Circlecircumscribing it , when every Angle of the

**Figure**, touches the Circumference ofthe circumscribing Circle . 2. A Right - lined

**Figure**is , then , said to circumscribea ...

Page 18

In this Process it may be observed , that not one Side of the

but only the Diagonals and Perpendiculars , all which fall within the

reason is obvious ; because the Sides are not at right angles with each other ; or

...

In this Process it may be observed , that not one Side of the

**Figure**is measured ,but only the Diagonals and Perpendiculars , all which fall within the

**Figure**. Thereason is obvious ; because the Sides are not at right angles with each other ; or

...

Page 19

E 1 Now , BI bisects the hexagonal

accidentally obtained . JK Fig . 2. Let K be the given Point , from which M HA a

Right Line is required to be drawn , bisecting the given

...

E 1 Now , BI bisects the hexagonal

**Figure**AC F ; but , the Points B and I areaccidentally obtained . JK Fig . 2. Let K be the given Point , from which M HA a

Right Line is required to be drawn , bisecting the given

**Figure**. Draw BF , and IH...

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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.