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

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Page 336

а a B G N. B. Not less than four Planes can form a

neceffarily be a Pyramid , and the Planes are all Triangles . Therefore a Pyramid

may be said to be the firit of Piane

. VIII .

а a B G N. B. Not less than four Planes can form a

**Solid**; and that , muftneceffarily be a Pyramid , and the Planes are all Triangles . Therefore a Pyramid

may be said to be the firit of Piane

**Solids**; nevertheless it is not the simplest . Def. VIII .

Page 355

If any two , of three given Plane Angles , be greater than the third , and the Lines

containing the Angles all equal ; and if those three Angles are , together , less

than four Right Angles , they will form a

joining ...

If any two , of three given Plane Angles , be greater than the third , and the Lines

containing the Angles all equal ; and if those three Angles are , together , less

than four Right Angles , they will form a

**solid**Angle ; and three Right Lines ,joining ...

Page 407

H A Sphere is equal , in its

the Surface of the Sphere , and its Altitude to the Radius . B Imagine the Sphere

ADF circumscribed E by any regular Body whatever ; and , from every Angle of

the ...

H A Sphere is equal , in its

**solid**Contents , to a Cone , whose Base is equal tothe Surface of the Sphere , and its Altitude to the Radius . B Imagine the Sphere

ADF circumscribed E by any regular Body whatever ; and , from every Angle of

the ...

Page 23

MENSURATION OF

the whole Business is to find a ... Figure is equal to ; fo , Mensuration of

consists in determining cubical Feet , & c . are contained in the proposed

MENSURATION OF

**SOLIDS**. how many a AS : S , in Mensuration of Superficies ,the whole Business is to find a ... Figure is equal to ; fo , Mensuration of

**Solids**consists in determining cubical Feet , & c . are contained in the proposed

**Solid**. Page 24

It is manifest , that if the

5 times ab , having equal thickness , it would contain the small Cube , a cb , 45

times , i.e. five times 9 ; and thus it will increase , as often as the measure ab is ...

It is manifest , that if the

**Solid**ACE ( being a Parallelopiped ) was longer , equal D5 times ab , having equal thickness , it would contain the small Cube , a cb , 45

times , i.e. five times 9 ; and thus it will increase , as often as the measure ab 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.