## 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 53

The Triangle GCD , is equal to the given

the Trap.FCDE is equal to the Pent . ABCDE . For , fince FB is parallel to AC , the

Triangle AFC is equal to ABC ( 18. 1. ) and ATC is common to both ; wherefore ...

The Triangle GCD , is equal to the given

**Pentagon**ABCDE . Ax . 7. 1 . Dem . Ift ;the Trap.FCDE is equal to the Pent . ABCDE . For , fince FB is parallel to AC , the

Triangle AFC is equal to ABC ( 18. 1. ) and ATC is common to both ; wherefore ...

Page 88

To construct a

ABF , on the extreme Point B. By the Table , the Angle of a

Angle in the ratio of 6 to 5 , difference 1 . With the Radius AB ( or any other ) on ...

To construct a

**Pentagon**, by the Table , on the Line AB . E 1 Make a Right Angle ,ABF , on the extreme Point B. By the Table , the Angle of a

**Pentagon**is to a RightAngle in the ratio of 6 to 5 , difference 1 . With the Radius AB ( or any other ) on ...

Page 221

To inscribe a regular

Isosceles Triangle , ABC , whose Angles BAC , ACB are , each , double the Angle

ABC Prop . I Bisect each of the Angles BAC , ACB by the Right Lines AD and CE

...

To inscribe a regular

**Pentagon**in a Circle . ABC is the given Circle . Inscribe anIsosceles Triangle , ABC , whose Angles BAC , ACB are , each , double the Angle

ABC Prop . I Bisect each of the Angles BAC , ACB by the Right Lines AD and CE

...

Page 222

E ΑΙ B PROPOSITION X. To describe a regular

ABCDE be the angular Points of D a

which draw the Tangents FG , GH , HI , & c . cuting each other , in F , G , H , I , and

K ...

E ΑΙ B PROPOSITION X. To describe a regular

**Pentagon**about a Circle . LetABCDE be the angular Points of D a

**Pentagon**, inscribed in a Circle , through Iwhich draw the Tangents FG , GH , HI , & c . cuting each other , in F , G , H , I , and

K ...

Page 8

E The

Circumfcribing Circle ; by the five Segments AGB , BD , & c . ID C Bisect the Ark

AGB and draw CG , which will be perpendicular to AB ; and draw the Chords AG ,

GB , which ...

E The

**Pentagon**ABDEF , it is evident , is less , in its Area , than theCircumfcribing Circle ; by the five Segments AGB , BD , & c . ID C Bisect the Ark

AGB and draw CG , which will be perpendicular to AB ; and draw the Chords AG ,

GB , which ...

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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.