## 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 115

Hence , it is plain that the Angles x , y and z , made with GE , are all equal to one

another ; and , being equal to one another , the Right Lines AB , CD and EF are

...

Hence , it is plain that the Angles x , y and z , made with GE , are all equal to one

another ; and , being equal to one another , the Right Lines AB , CD and EF are

**consequently**parallel between themselves , 4. Again ; since the Angles x , y and...

Page 223

Then , in the Triangles EBF , FBG ; FBo = FEO + EBO , and , FB O = FGO + BGO ;

wherefore , EBO = BGO ;

the ...

Then , in the Triangles EBF , FBG ; FBo = FEO + EBO , and , FB O = FGO + BGO ;

**consequently**, FE + EB O = FG0 + BGO . - Ax.3.1 But , EB = BG ( Ax . 1. 1. )wherefore , EBO = BGO ;

**consequently**, EFQ = FGo ; and , therefore EF = FB , Inthe ...

Page 341

1 . and CB = BD ; wh . the Triangle CBG = DBH ; and ,

and BG = BH . Wherefore , in the Triangles CAG , DAH ; AC , CG , are

sespectively equal to AD , DH , and contain equal Angles ;

equal to AH ...

1 . and CB = BD ; wh . the Triangle CBG = DBH ; and ,

**consequently**, CG = DH ,and BG = BH . Wherefore , in the Triangles CAG , DAH ; AC , CG , are

sespectively equal to AD , DH , and contain equal Angles ;

**consequently**, AG isequal to AH ...

Page 9

From all which , it is clear , that every Poligon , inscribed in a Circle , is less than

the Circle , by as many Segments as the Poligon has Sides ; and

every Poligon , circuim fcribed , is greater than the Circle . But , the greater the ...

From all which , it is clear , that every Poligon , inscribed in a Circle , is less than

the Circle , by as many Segments as the Poligon has Sides ; and

**consequently**,every Poligon , circuim fcribed , is greater than the Circle . But , the greater the ...

Page 25

B E C But , the Perpendicular BF , is 3 Feet and 8 Inches ;

Solid will contain 41-4 , 3 times and two thirds , ( 8 Inches , being two thirds of a

Foot . ) Wherefore , 41 Feet , 4 Inches multiplied 3 times , and two thirds , equal

151 ...

B E C But , the Perpendicular BF , is 3 Feet and 8 Inches ;

**consequently**, theSolid will contain 41-4 , 3 times and two thirds , ( 8 Inches , being two thirds of a

Foot . ) Wherefore , 41 Feet , 4 Inches multiplied 3 times , and two thirds , equal

151 ...

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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.