Orchard Planting Problem/Historical Note

Historical Note on the Orchard Planting Problem
The Orchard Planting Problem appears to have first been set by in his $1821$ collection, where he worded it poetically as:


 * 1. Your aid I want, nine trees to plant
 * In rows just half a score;
 * And let there be in each row three.
 * ''Solve this: I ask no more.


 * 2. Fain would I plant a grove in rows
 * But how must I its form compose
 * With three trees in each row;
 * To have as many rows as trees;
 * Now tell me, artists, if you please;
 * 'Tis all I want to know.


 * 3. Ingenious artists, if you please
 * To plant a grove, pray show,
 * In twenty-three rows with fifteen trees
 * ''And three in every row.


 * 4. It is required to plant $17$ trees in $24$ rows,

and to have $3$ trees in every row.


 * 5. Ingenious artists, pray dispose
 * Twenty-four trees in twenty-four rows.
 * Three trees I'd have in every row;
 * A pond in midst I'd have also.
 * A plan thereof I fain would have,
 * And therefore your assistance crave.


 * 6. Fam'd arborists, display your power
 * And show how I may plant a bower
 * With verdant fir and yew:
 * Twelve trees of each I would dispose,
 * In only eight-and-twenty rows;
 * Four trees in each to view.


 * 7. Plant $27$ trees in $15$ rows, $5$ to a row.


 * 8. Ingenious artists, if you please,
 * Now plant me five-and-twenty trees,
 * In twenty-eight rows, nor less, nor more;
 * In some rows five, some three, some four.


 * 9. It is required to plant $90$ trees in $10$ rows, with $10$ trees in each row; each tree equidistant from the other, also each row equidistant from a pond in the centre.


 * 10. A gentleman has a quadrangular irregular piece of ground, in which he is desirous of planting a quincunx, in such a manner, that all the rows of trees, whether transversal or diagonal, shall all be right lines. How must this be done?


 * Note: A real quincunx is a plantation of trees disposed in a square, consisting of five trees, one at each corner, and the fifth in the middle; but in the present case, the trees are to be disposed in a quadrangle, one at each corner (as in the square), and the fifth at the point of intersection of the two diagonals.