## 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 4

In demonstrating fome Theorems , it is necessary to have recourse , frequently ,

to suppose

the consequences , arising from

...

In demonstrating fome Theorems , it is necessary to have recourse , frequently ,

to suppose

**such**and**such**things , which are not so in reality ; by the absurdity ofthe consequences , arising from

**such**a supposition , a conclusion is drawn , and...

Page 5

always be made of

Properties , of which , being previously demonstrated . DEMONSTRATION .

When any thing is proposed , or affirmed in a Propofition , the Case is first stated

and ...

always be made of

**such**Figures or Lines as are already well understood ; theProperties , of which , being previously demonstrated . DEMONSTRATION .

When any thing is proposed , or affirmed in a Propofition , the Case is first stated

and ...

Page 110

... to me ,

for granted . This Book is much encumbered with useless Demonstrations , of

feveral Propositions , already fully demonstrated or need none ; for , what is

evident ...

... to me ,

**such**a necessary consequence , that I would not hesitate to take themfor granted . This Book is much encumbered with useless Demonstrations , of

feveral Propositions , already fully demonstrated or need none ; for , what is

evident ...

Page 238

Incommensurable Quantities are

there cannot be found any determinate Quantity , how small soever , which ,

being multiplied , will be equal to each of the other ; but that there will be a

deficiency ...

Incommensurable Quantities are

**such**as no other Quantity can measure ; i , e ,there cannot be found any determinate Quantity , how small soever , which ,

being multiplied , will be equal to each of the other ; but that there will be a

deficiency ...

Page 240

Wherefore ,

and can have no Ratio to one another . N. B. The Ratio of two Quantities is not

expressed by the deficiency or excess of the Antecedent to the Consequent ...

Wherefore ,

**such**Quantities as are not of the same kind , are heterogeneous ,and can have no Ratio to one another . N. B. The Ratio of two Quantities is not

expressed by the deficiency or excess of the Antecedent to the Consequent ...

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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.