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

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Page iv

The 16th and 17th Propositions , Bock ift , are entirely useless ; for since , in the

32nd , the external Angle is

absurd to

The 16th and 17th Propositions , Bock ift , are entirely useless ; for since , in the

32nd , the external Angle is

**proved**to be ... are equal to two right ones ; it seemsabsurd to

**prove**, before hand , that any two of the Angles are less than two right ... Page 269

1 none have given a Demonstration of Inverse Ratio ; which being

Converse Ratio is also

that Euclid should not demonstrate either ; also , that he should

1 none have given a Demonstration of Inverse Ratio ; which being

**proved**, everyConverse Ratio is also

**proved**. ... But what , to me , seems very extraordinary is ,that Euclid should not demonstrate either ; also , that he should

**prove**( if it may ... Page 342

6 Euclid . If two Right Lines be perpendicular to the same Plane , they are parallel

to one another . This might well pass for an Axiom ; for , it is evident , the two

Lines may be in the fame Plane , which is thus

right ...

6 Euclid . If two Right Lines be perpendicular to the same Plane , they are parallel

to one another . This might well pass for an Axiom ; for , it is evident , the two

Lines may be in the fame Plane , which is thus

**proved**. Ic Let AB and CD be atright ...

Page 388

If they are Parallelopipeds , it is already

Parallelopiped ( is a Prism ; Def . 7. 7. ) may be divided , by a Plane pasiing

through its opposite Diagonals , into two equal and similar triangular Prilins ;

consequently ...

If they are Parallelopipeds , it is already

**proved**- Cor . 1.17.7 . For , everyParallelopiped ( is a Prism ; Def . 7. 7. ) may be divided , by a Plane pasiing

through its opposite Diagonals , into two equal and similar triangular Prilins ;

consequently ...

Page 389

1. Cylinders , having equal Altitudes , have the same Ratio to each ather as their

Bases . For , similar Poligons , inscribed in Circles , are , to each other , as the

Squares of their Diameters . Th . 14. 6 . And it has been

1. Cylinders , having equal Altitudes , have the same Ratio to each ather as their

Bases . For , similar Poligons , inscribed in Circles , are , to each other , as the

Squares of their Diameters . Th . 14. 6 . And it has been

**proved**, that all Prisons ...### What people are saying - Write a review

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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.