## 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 101

The Ruler being now in the position of the Conjugate Diameter ; the Pin , at F , in

the

af F , being now supposed to be in the

...

The Ruler being now in the position of the Conjugate Diameter ; the Pin , at F , in

the

**Center**, and that at G fallen down to g ; the motion is continued to B ; the Pinaf F , being now supposed to be in the

**Center**, moves towards B , and the Pin at...

Page 178

Axiom ift , All Lines drawn from the

equal . As EA , EC , & c . For , they are all Radii or Semidiameters . 2nd . Two or

more Diameters , of a Circle , mutually bisect each other . For they all pass

through ...

Axiom ift , All Lines drawn from the

**Center**of a Circle to the Circumference areequal . As EA , EC , & c . For , they are all Radii or Semidiameters . 2nd . Two or

more Diameters , of a Circle , mutually bisect each other . For they all pass

through ...

Page 180

If a Right Line , drawn through the

drawn through the

Right Line DE pass through C , 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 theRight Line DE pass through C , the

**Center**, dividing the Chord Line AB into two ... Page 189

If two Circles touch each other , a Right Line , joining their

through the Point of contact of the two Circles . First ; let AB and AH be two

Circles , touching each other , inwardly , in A. C is the

AB .

If two Circles touch each other , a Right Line , joining their

**Centers**, will passthrough the Point of contact of the two Circles . First ; let AB and AH be two

Circles , touching each other , inwardly , in A. C is the

**Center**of the lesser Circle ,AB .

Page 229

And , fince the Angle C , at the

Degrees , consequently , the two remaining Angles , CAB , CBA , at the Base ,

being equal ( 9. 1. ) they are , each , equal to half the difference between the

Angle ACB ...

And , fince the Angle C , at the

**Center**of the Triangle ACB , is equal to 40Degrees , consequently , the two remaining Angles , CAB , CBA , at the Base ,

being equal ( 9. 1. ) they are , each , equal to half the difference between the

Angle ACB ...

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A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... Thomas Malton No preview available - 2016 |

### 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.