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

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Page 47

For , it is half the Rectangle A EFC , which is double the Area of the

. - 17. I. N. B. If any other angled Parallelogram was required , you muft proceed

as in Prob . 19. making the Angle CDG or DCF equal to the Angle given ; ftill ...

For , it is half the Rectangle A EFC , which is double the Area of the

**Triangle**ABC. - 17. I. N. B. If any other angled Parallelogram was required , you muft proceed

as in Prob . 19. making the Angle CDG or DCF equal to the Angle given ; ftill ...

Page 53

The

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

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 55

The

Pentagon , KGLDC . 18. 1 . Then ; produce the Side CD ; and , from the Angle L ,

draw LM , parallel to the Diagonal GD ; cuting CD produced , in M , and draw GM

.

The

**Triangle**FLD is equal to FED . The given Figure is now reduced to aPentagon , KGLDC . 18. 1 . Then ; produce the Side CD ; and , from the Angle L ,

draw LM , parallel to the Diagonal GD ; cuting CD produced , in M , and draw GM

.

Page 133

Hence , if one Angle of a

one . For , if either Side , containing the Right Angle , be produced ; the external

Angle , being equal to the two remote ones , is equal to the Right Angle to which

it ...

Hence , if one Angle of a

**Triangle**be equal to the other two Angles , it is a Rightone . For , if either Side , containing the Right Angle , be produced ; the external

Angle , being equal to the two remote ones , is equal to the Right Angle to which

it ...

Page 213

Thomas Malton. b d Otherwise : Draw at pleasure a d , cuting the Cir cumference

in a and d . Make the Angle , adc , equal to B , & join a c . Make , cab , equal to

the AngleA , & join bc . The

Thomas Malton. b d Otherwise : Draw at pleasure a d , cuting the Cir cumference

in a and d . Make the Angle , adc , equal to B , & join a c . Make , cab , equal to

the AngleA , & join bc . The

**Triangle**abc is equiangular to the a**Triangle**ABC .### What people are saying - Write a review

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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.