## 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 ii

better purpose . For , what has methanic Trades to do with Latin ? any more than

a common Porter or Carman with Logic ; it may indeed complete him a Pedant or

Coxcomb , but can never be of real

...

better purpose . For , what has methanic Trades to do with Latin ? any more than

a common Porter or Carman with Logic ; it may indeed complete him a Pedant or

Coxcomb , but can never be of real

**use**in his Profession ; even suppose he had...

Page 19

In the 23d Des finition they are , in general , called many - sided Figures ; ' tis a

itrange ungeometrical Term , and never once made

are affumed . Euclid , himself , has not defined a Parallelogram , that most

ful ...

In the 23d Des finition they are , in general , called many - sided Figures ; ' tis a

itrange ungeometrical Term , and never once made

**use**of after , but other Termsare affumed . Euclid , himself , has not defined a Parallelogram , that most

**use**.ful ...

Page 50

N. B. By this Problem and the last may be performed the 45th of Euclid , without

the assistance of the next , which he makes

the Parallelogram un der a given Angle , as hikl , which is equal to HIKL by the

last ...

N. B. By this Problem and the last may be performed the 45th of Euclid , without

the assistance of the next , which he makes

**use**of , and much readier ; makingthe Parallelogram un der a given Angle , as hikl , which is equal to HIKL by the

last ...

Page 242

It was not the Design , of those Geometers who made

Analogy , in abstract , but only , to explain what is meant by analogy of Ratios (

between two and two Quantities ) which is a very proper and expressive Term ,

for ...

It was not the Design , of those Geometers who made

**use**of this Term , to defineAnalogy , in abstract , but only , to explain what is meant by analogy of Ratios (

between two and two Quantities ) which is a very proper and expressive Term ,

for ...

Page 30

As the Line of Chords , and its

a Description of it may not be unnecessary . And first , I will thew how to construct

a Line of Chords . 40 50 fo a 70 With any Radius , at Discretion , as AC , B on C ...

As the Line of Chords , and its

**Use**, is better known than understood , I presume ,a Description of it may not be unnecessary . And first , I will thew how to construct

a Line of Chords . 40 50 fo a 70 With any Radius , at Discretion , as AC , B on C ...

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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.