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

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Page 142

The two Diagonals of a Parallelogram

divides a Parallelogram into two equal and congruous Figures . G In the

Parallelogram ABCD , draw the Diagonals , AC and BD . I say the Diagonal AC is

The two Diagonals of a Parallelogram

**bisect**each other . And , every Diameterdivides a Parallelogram into two equal and congruous Figures . G In the

Parallelogram ABCD , draw the Diagonals , AC and BD . I say the Diagonal AC is

**bisected**... Page 172

If any Side of a Triangle is

Angle to the bifcêting Point ; the Squares of the other two Sides of the Triangle ,

will be equal to twice the Square of the

If any Side of a Triangle is

**bisected**, and a Right Line be drawn from the oppositeAngle to the bifcêting Point ; the Squares of the other two Sides of the Triangle ,

will be equal to twice the Square of the

**bisecting**Line , added to half the Square ... Page 181

Euclid , AA if , in a Circle , two Chord Lines cut each other , and are not both

drawn through the Center , they cannot

be two Chord Lines cuting each other , in E. АВ If one of them , CD ( Fig . 1. )

passeth ...

Euclid , AA if , in a Circle , two Chord Lines cut each other , and are not both

drawn through the Center , they cannot

**bisect**each other . F.2 . Let AB and , CDbe two Chord Lines cuting each other , in E. АВ If one of them , CD ( Fig . 1. )

passeth ...

Page 284

And , conversely , if any Side of a Triangle be cut , in the proportion of the other

two Sides ; and if the greater Segment be contiguous to the greater Side ; then

will a Right Line , drawn from the point of section to the opposite Angle ,

...

And , conversely , if any Side of a Triangle be cut , in the proportion of the other

two Sides ; and if the greater Segment be contiguous to the greater Side ; then

will a Right Line , drawn from the point of section to the opposite Angle ,

**bisect**Ey...

Page 326

If all the Sides of a Trapezium are bifected , and the Points of

contiguous Sides , are joined by Right Lines , the ... B G K M Let the sides of the

Trapezium , ABCD , be

GH ...

If all the Sides of a Trapezium are bifected , and the Points of

**bisection**, incontiguous Sides , are joined by Right Lines , the ... B G K M Let the sides of the

Trapezium , ABCD , be

**bisected**in the Points E , F , G , and H , and draw EF , FG ,GH ...

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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.