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

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Page 39

In returning , or breaking Mouldings at an Angle , whether external or internal ,

the Angle bisected is the Mitre ; in which the Mouldings will exactly fit each other .

PROBLEM X. To make a Right Angle ; or , to draw a Perpendicular at the

...

In returning , or breaking Mouldings at an Angle , whether external or internal ,

the Angle bisected is the Mitre ; in which the Mouldings will exactly fit each other .

PROBLEM X. To make a Right Angle ; or , to draw a Perpendicular at the

**extreme**...

Page 267

... seeing that there is equal Ratios between the two

; let the intermediate Ratios be ever so many , and in what order foever , provided

there be an equal number in each Rank ; and the

... seeing that there is equal Ratios between the two

**extremes**, A and G , H and F; let the intermediate Ratios be ever so many , and in what order foever , provided

there be an equal number in each Rank ; and the

**extreme**Ratios are equal ... Page 329

The Diagonal of a regular Pentagon is to its Side , as a Line divided in

and mean Proportion . In the Pentagon A B C D E , let the two Diagonals , AD and

BE , be drawn , cuting each other in F. B. Then , A D is to AB , or AE , as A E is to ...

The Diagonal of a regular Pentagon is to its Side , as a Line divided in

**extreme**and mean Proportion . In the Pentagon A B C D E , let the two Diagonals , AD and

BE , be drawn , cuting each other in F. B. Then , A D is to AB , or AE , as A E is to ...

Page 330

The Diameter or Perpendicular , of a regular Pentagon , is divided in

mean Proportions by ' a Diagonal ... I say , that CF is divided in

mean Proportion , in G. Draw EH parallel to CF ; also , the Diagonal BE , cuting

the ...

The Diameter or Perpendicular , of a regular Pentagon , is divided in

**extreme**andmean Proportions by ' a Diagonal ... I say , that CF is divided in

**extrémë**andmean Proportion , in G. Draw EH parallel to CF ; also , the Diagonal BE , cuting

the ...

Page 331

Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...

Thomas Malton. Hence , if a Right Line be divided in

Proportion , and from cither

less is ...

Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ...

Thomas Malton. Hence , if a Right Line be divided in

**extreme**and meanProportion , and from cither

**extreme**of the greater Segment the measure of theless is ...

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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.