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

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Page 180

If a Right Line , drawn through the Center of a Circle , bisects a

drawn through the Center , it will cut it perpendicularly . In the Circle ADB ; let the

Right Line DE pass through C , the Center , dividing the

If a Right Line , drawn through the Center of a Circle , bisects a

**Chord**Line , notdrawn through the Center , it will cut it perpendicularly . In the Circle ADB ; let the

Right Line DE pass through C , the Center , dividing the

**Chord**Line AB into two ... Page 182

Equal

Lines which are equi - distant , are equal . B HA 16 Let AB and CD be equal

E.

Equal

**Chord**Lines , in a Circle , are equally distant from the Center ; and**Chord**Lines which are equi - distant , are equal . B HA 16 Let AB and CD be equal

**Chord**Lines in the Circle ADB . I I say , they are equally distant from the Center ,E.

Page 30

The Line of

construct a Line of

, as a Center , transfer all the Measures on the Ark , to the

Figure ...

The Line of

**Chords**, and its Use , explained . ... And first , I will thew how toconstruct a Line of

**Chords**. ... Draw the**Chord**Line AB ; and , from the extreme A, as a Center , transfer all the Measures on the Ark , to the

**Chord**AB , as in theFigure ...

Page 31

For ADC is an Equilateral Triangle , whose Angles are all equal , and

consequently , the

be required ; from A make AB , equal to the whole Line of

and draw ...

For ADC is an Equilateral Triangle , whose Angles are all equal , and

consequently , the

**Chord**, AD , is equal to the Radius AC - 11.4 . If a Right Anglebe required ; from A make AB , equal to the whole Line of

**Chords**of go Degrees ,and draw ...

Page 32

A The

the

more ; for the

...

A The

**Chord**of 19 Degrees , it is evident , deviates very little from a Right Line ;the

**Chord**of 30 Degrees deviates considerably , and AD , the**Chord**of 60 , stillmore ; for the

**Chord**AD , of 60 , and the two**Chords**of 30 make a Triangle , AED...

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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.