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

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Page

I I may appear fomewhat ftrange to call fo copious a Work as this , an Abridgment

; which , on examination , and comparing with those who have transcribed

, will be found to be a great abridgment of the Elements , both in the number of ...

I I may appear fomewhat ftrange to call fo copious a Work as this , an Abridgment

; which , on examination , and comparing with those who have transcribed

**Euclid**, will be found to be a great abridgment of the Elements , both in the number of ...

Page 19

neceffary Figure . I admire Mr. Stone's ... increase the Number , unnecessarily ;

and says , that

indeed ...

**Euclid**, himself , has not defined a Parallelogram , that most use . ful andneceffary Figure . I admire Mr. Stone's ... increase the Number , unnecessarily ;

and says , that

**Euclid**has sufficiently defined it in the 34th Proposition . Mr. Stoneindeed ...

Page 270

If what I have advanced , on the sublime Doctrine of Pro . portion , be not

sufficient , for any purpose whatever , I will be bold to say , that it is not so in

gathered from the ...

If what I have advanced , on the sublime Doctrine of Pro . portion , be not

sufficient , for any purpose whatever , I will be bold to say , that it is not so in

**Euclid**, or any of his Commentators , The Axioms , which I have given , aregathered from the ...

Page 311

I. 24 Few , if any , who have favoured the World with Treatises on Geometry ,

have taken notice of this Theorem , or the foregoing , ( the 27 . and the of

except those who have trod in his path without fteping the least aside ; indeed , it

...

I. 24 Few , if any , who have favoured the World with Treatises on Geometry ,

have taken notice of this Theorem , or the foregoing , ( the 27 . and the of

**Euclid**)except those who have trod in his path without fteping the least aside ; indeed , it

...

Page 356

N.B. The last part of this Theorem , which ( according to

that , unless two of the Plane Angles are greater than the third , a Triangle cannot

be formed of the three Lines , joining the extremes of equal Sides ; whereas ...

N.B. The last part of this Theorem , which ( according to

**Euclid**) seems to imply ,that , unless two of the Plane Angles are greater than the third , a Triangle cannot

be formed of the three Lines , joining the extremes of equal Sides ; whereas ...

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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.