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

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Page iii

I have perused several Authors on the Subject , and find , that

it in a manner scarce intelligible to a beginner , unless he has

of Algebra ; others would be better understood and approved , if they did not ...

I have perused several Authors on the Subject , and find , that

**some**have treatedit in a manner scarce intelligible to a beginner , unless he has

**some**knowledgeof Algebra ; others would be better understood and approved , if they did not ...

Page v

I shall ever be of opinion with Tacquet , and

formal Demonstration of Propositions which are self - evident , is involving a thing

, in itself clear and conspicuous , in darkness and obscurity . I have always found

...

I shall ever be of opinion with Tacquet , and

**some**others , that , to attempt aformal Demonstration of Propositions which are self - evident , is involving a thing

, in itself clear and conspicuous , in darkness and obscurity . I have always found

...

Page vi

I have given it the first place , contrary to

Book , or otherwise disposed of it . By which means , we are frequently at a loss

in the References , and are told to form ConAructions , before we have learned ...

I have given it the first place , contrary to

**some**others who have made it the lastBook , or otherwise disposed of it . By which means , we are frequently at a loss

in the References , and are told to form ConAructions , before we have learned ...

Page 179

For , if the Circles , AD and BD , touched inwardly , in more than a Point , as at D ,

the Curve of the lesser Circle , AD , must coincide in

curve of the larger Circle , BD , which , from the genefis of a Circle ; cannot be ...

For , if the Circles , AD and BD , touched inwardly , in more than a Point , as at D ,

the Curve of the lesser Circle , AD , must coincide in

**some**part , entirely , with thecurve of the larger Circle , BD , which , from the genefis of a Circle ; cannot be ...

Page 4

... F , F , & c . and

Triangles , as cc , & c . Now , it would be no easy matter to ascertain how many

entire Squares all those irregular Figures are equal to ; for there are but 12 ,

entire ...

... F , F , & c . and

**some**Pentagons , as a , a ;**some**Trapezia , as bb , and**some**Triangles , as cc , & c . Now , it would be no easy matter to ascertain how many

entire Squares all those irregular Figures are equal to ; for there are but 12 ,

entire ...

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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.