## 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 116

Now since all these properties of Right Lines , and of Angles

Lines , are manifest , from what has been advanced already , there is , I think , but

little occasion for Demonstration ; nevertheless , in conformity to the Antients , I ...

Now since all these properties of Right Lines , and of Angles

**formed**by RightLines , are manifest , from what has been advanced already , there is , I think , but

little occasion for Demonstration ; nevertheless , in conformity to the Antients , I ...

Page 150

In respect of the properties of Right Lines , and Angles

Intersections , in the first lix Theorems , the knowledge of which , though in a

manner self - evident , is absolutely necessary for attaining the properties of

Figures . I shall just ...

In respect of the properties of Right Lines , and Angles

**formed**by theirIntersections , in the first lix Theorems , the knowledge of which , though in a

manner self - evident , is absolutely necessary for attaining the properties of

Figures . I shall just ...

Page 355

EFG Then , a solid Angle may be

of the three Lines , AC , AD , and EC , a Triangle may be

over the Triangles A F B and BGC ( equal ABD and EBC ) till the two Sides BF

and ...

EFG Then , a solid Angle may be

**formed**of those three Angles , ABC , & c . alfo ,of the three Lines , AC , AD , and EC , a Triangle may be

**formed**. DEM . Turnover the Triangles A F B and BGC ( equal ABD and EBC ) till the two Sides BF

and ...

Page 356

Or , a solid Angle

than all the others , added together . Nothwithstanding , if BF and BG be equal to

AB & BC respectively , although the Angles ( ABF , CBG ) are together , less than

...

Or , a solid Angle

**formed**of any number of Plane Angles , any one must be lessthan all the others , added together . Nothwithstanding , if BF and BG be equal to

AB & BC respectively , although the Angles ( ABF , CBG ) are together , less than

...

Page 407

B Imagine the Sphere ADF circumscribed E by any regular Body whatever ; and ,

from every Angle of the circumscribing solid suppose Right Lines , AC , EC , & c .

drawn to the Center , C ; there will be

B Imagine the Sphere ADF circumscribed E by any regular Body whatever ; and ,

from every Angle of the circumscribing solid suppose Right Lines , AC , EC , & c .

drawn to the Center , C ; there will be

**formed**as many Pyramids , as the Solid ...### 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.