## 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 28

28 INSTRUCTIONS F : 0 R YOUNG S T U D E N T S. I would advise the young

Practitioner to draw every Figure as he proceeds ; carefully remarking what

things , as Points ,

stronger ...

28 INSTRUCTIONS F : 0 R YOUNG S T U D E N T S. I would advise the young

Practitioner to draw every Figure as he proceeds ; carefully remarking what

things , as Points ,

**Lines**, Angles , & c . are**given**; which are , in general ,stronger ...

Page 30

To draw Right Line from a Point given , C , which shall be equal to a

A B. D Extend or open the Compasses equal to the Line given ; fix one of their

Points in C , the given Point , and , with the other , describe a Circle , or portion of

a ...

To draw Right Line from a Point given , C , which shall be equal to a

**given Line**;A B. D Extend or open the Compasses equal to the Line given ; fix one of their

Points in C , the given Point , and , with the other , describe a Circle , or portion of

a ...

Page 34

To draw a Line through a given Point , which shall be parallel to a Right Line

given . с A Pr . 3 O AB is the

draw at pleasure a Right Line , as CB , culing the

B ...

To draw a Line through a given Point , which shall be parallel to a Right Line

given . с A Pr . 3 O AB is the

**given Line**, and C is the Point given . Through C ,draw at pleasure a Right Line , as CB , culing the

**given Line**, AB , in the point B.B ...

Page 72

AB is the

2 , and 3 . ... and FD equal , respectively , to the Divisions on Z. Through the

extreme Points of the two Lines , AB and CD , draw CA and DB , produced th till

they ...

AB is the

**given Line**; and Z , is a Line divided in the Pro , portion required , at 1 ,2 , and 3 . ... and FD equal , respectively , to the Divisions on Z. Through the

extreme Points of the two Lines , AB and CD , draw CA and DB , produced th till

they ...

Page 209

A and B are the assumed Points ; and , let CD be a

required to find the Point D , fo , that , if two Right

to that Point , the Angle ADB , ihall be greater than any other Angle , made D by

Right ...

A and B are the assumed Points ; and , let CD be a

**given**Right**Line**. It isrequired to find the Point D , fo , that , if two Right

**Lines**AD and BD be E drawn ,to that Point , the Angle ADB , ihall be greater than any other Angle , made D by

Right ...

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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.